1+9+9^2+9^3+....+9^k= 1/2* ((3^k)-1)/2)((3^k+1)+1)/2) is true for all the k`s

n=((3^k)-1))/2

Sum geometric sequence is easy. I skipped that part.

I had just replaced n by its value so the equation become a pure identity.

It that correct?

## Search found 431 matches

- Wed Aug 24, 2016 8:24 pm UTC
- Forum: Mathematics
- Topic: Goahead52's Math Posts
- Replies:
**148** - Views:
**19028**

- Wed Aug 24, 2016 5:16 pm UTC
- Forum: Mathematics
- Topic: Goahead52's Math Posts
- Replies:
**148** - Views:
**19028**

### Re: Goahead52's Math Posts

Knowing what is an identity as I said will not help me to solve any problem. When things are not really helpful it is simple : I ignore them. You know what is an identity and what is an equation good for you. Fine! you are serious mathematician with huge knowledge I do not even discuss it. Does this...

- Wed Aug 24, 2016 4:25 pm UTC
- Forum: Mathematics
- Topic: Goahead52's Math Posts
- Replies:
**148** - Views:
**19028**

### Re: Goahead52's Math Posts

If I replace n by something related to 9 and its powers it will become an identity. You will learn nothing from it. Out of curiosity, could you do so please? You can do it by yourself just by finding n. You surely know how to sum geometric sequence. Hence it will be done in few seconds. Anyway I de...

- Wed Aug 24, 2016 3:09 pm UTC
- Forum: Mathematics
- Topic: Goahead52's Math Posts
- Replies:
**148** - Views:
**19028**

### Re: Goahead52's Math Posts

If I replace n by something related to 9 and its powers it will become an identity. You will learn nothing from it. In my point of view the distinction between identity and equation is meaningless when it comes to solving any problem. Many distinctions are unhelpful when it comes to attacking a prob...

- Wed Aug 24, 2016 1:51 pm UTC
- Forum: Mathematics
- Topic: Goahead52's Math Posts
- Replies:
**148** - Views:
**19028**

### Re: Goahead52's Math Posts

The sum 1+9+9^2+9^3+9^4...+9^k is always a triangular number

Is it an identity or an equation?

Thank you for any comment.

Is it an identity or an equation?

Thank you for any comment.

- Tue Aug 23, 2016 12:00 pm UTC
- Forum: Mathematics
- Topic: Goahead52's Math Posts
- Replies:
**148** - Views:
**19028**

### Re: Goahead52's Math Posts

It is not about mastering English or no. The difference between an identity and an equation is meaningless. y=y is apparently an identity. It show you "nothing" but all depend on what you are going to put on y. y could be represent an infinite number of ways. Any equation no matter how com...

- Mon Aug 22, 2016 8:34 pm UTC
- Forum: Mathematics
- Topic: Goahead52's Math Posts
- Replies:
**148** - Views:
**19028**

### Re: Goahead52's Math Posts

Here is what he said : "If you don't know what a mathematical identity is, then you are not in a position to reject WIkipedia because it contains occasional errors." It said it all! The teacher talking to alumnis. I`m not an alumni. I know wikipedia since the beginning and I have seen many...

- Mon Aug 22, 2016 8:19 pm UTC
- Forum: Mathematics
- Topic: Goahead52's Math Posts
- Replies:
**148** - Views:
**19028**

### Re: Goahead52's Math Posts

Definitions are not false. They are definitions. They can't be false, because that is not how definitions work. The statement "A(A-y+1) mod (A-2)=A-(2*y)+4" is true for all A and all y. It therefore can tell us nothing about A or about y, just like "x=x" tells us nothing about t...

- Mon Aug 22, 2016 8:07 pm UTC
- Forum: Mathematics
- Topic: Goahead52's Math Posts
- Replies:
**148** - Views:
**19028**

### Re: Goahead52's Math Posts

Please stop triple-posting. You can edit your last post if it's still the most recent post in a thread. If an identity tells you nothing about a variable, then it doesn't tell you anything useful about that variable. How do you know that the same variable could be written differently using even ext...

- Mon Aug 22, 2016 7:51 pm UTC
- Forum: Mathematics
- Topic: Goahead52's Math Posts
- Replies:
**148** - Views:
**19028**

### Re: Goahead52's Math Posts

How do you know what is useful and what is not when you do not know what I will do with such unuseful identity in your point of view?

- Mon Aug 22, 2016 7:48 pm UTC
- Forum: Mathematics
- Topic: Goahead52's Math Posts
- Replies:
**148** - Views:
**19028**

### Re: Goahead52's Math Posts

Each one here and elsewhere has the right to have his point of view about Wikipedia.

No one has the right to tell me what I have to think about Wikipedia no matter who he is.

No one has the right to tell me what I have to think about Wikipedia no matter who he is.

- Mon Aug 22, 2016 7:45 pm UTC
- Forum: Mathematics
- Topic: Goahead52's Math Posts
- Replies:
**148** - Views:
**19028**

### Re: Goahead52's Math Posts

Wikipedia is a fine place to reference for very basic mathematical ideas, such as the definition of identity. If you don't know what a mathematical identity is, then you are not in a position to reject WIkipedia because it contains occasional errors. The reason to reject your equation because it's ...

- Mon Aug 22, 2016 4:32 pm UTC
- Forum: Mathematics
- Topic: Goahead52's Math Posts
- Replies:
**148** - Views:
**19028**

### Re: Goahead52's Math Posts

Phi(x) of all those numbers is equal to 160 187 205 328 352 374 400 410 440 492 528 600 660 Why? Imagine that you have to factorize 187 and you know that 400 which is easy to factorize has its Euler totient such as phi(187)=phi(400) then you factorize 187 easily. That is just one hint to approximate...

- Mon Aug 22, 2016 4:29 pm UTC
- Forum: Mathematics
- Topic: Goahead52's Math Posts
- Replies:
**148** - Views:
**19028**

### Re: Goahead52's Math Posts

Do not forget that the way to handle the right part and the left part of any equation could lead you to solving it. How did I handle such equation is another debate? For those who are asking me about how to know phi(n) without factorizing it? Hint : many numbers have the same value of phi(n). If you...

- Mon Aug 22, 2016 4:22 pm UTC
- Forum: Mathematics
- Topic: Goahead52's Math Posts
- Replies:
**148** - Views:
**19028**

### Re: Factorization of odd semi prime is over!

Any equation is an identity except you need to isolate some variables to make it solvable. No it's not. Identity is a mathematical term that means: An identity is a statement resembling an equation which is true for all possible values of the variable(s) it contains. What is this? A(A-y+1) mod (p*q...

- Mon Aug 22, 2016 3:47 pm UTC
- Forum: Mathematics
- Topic: Goahead52's Math Posts
- Replies:
**148** - Views:
**19028**

### Re: Factorization of odd semi prime is over!

A(A-y+1) mod (p*q-2)=A-(2*y)+4 Since pq=A, we get that A(A-y+1) = A - 2y + 4 (mod (A-2)). Since A is congruent to 2 mod A-2, we find that 2(2-y+1) = 2-2y+4 (mod (A-2)). But this is an identity. That is to say, it's true for any values of A and y. So its truth doesn't tell us anything about y. Right...

- Mon Aug 22, 2016 3:42 pm UTC
- Forum: Mathematics
- Topic: Goahead52's Math Posts
- Replies:
**148** - Views:
**19028**

### Re: Factorization of odd semi prime is over!

knowing that n=pq is odd semiprime there is a solution to : 1. approximate phi(n)=2x 2. approximate y As we know that 2x+y=a (with a known) 1. How do you approximate phi(n) without factoring n in the first place? 2. What is y and how do you approximate it? 3. What is a? a was yet given if you read ...

- Mon Aug 22, 2016 12:06 pm UTC
- Forum: Logic Puzzles
- Topic: Factorial puzzle
- Replies:
**6** - Views:
**3813**

### Re: Factorial puzzle

Thank you for pointing out to something even before creating the EFN. Anyway any factorial could written in many ways as product of 2 EFN. Building a quick algorithm to represent k!=F(n,m) where F(n,m) is a function depending on 2 variables is not hard. But finding links between n and m is too hard....

- Mon Aug 22, 2016 11:59 am UTC
- Forum: Mathematics
- Topic: Goahead52's Math Posts
- Replies:
**148** - Views:
**19028**

### Re: Factorization of odd semi prime is over!

knowing that n=pq is odd semiprime there is a solution to : 1. approximate phi(n)=2x 2. approximate y As we know that 2x+y=a (with a known) then we will obtain the definitive solution by convergence. We will go quickly to the solution. We coud reduce the global equation 2x+y=a to more handable equat...

- Mon Aug 22, 2016 11:41 am UTC
- Forum: Mathematics
- Topic: Goahead52's Math Posts
- Replies:
**148** - Views:
**19028**

### Re: Factorization of odd semi prime is over!

I got it!!! After simplification I obtained a final (it could be improved) formula : 2x+y=a (where is a is known and more important 2x is equal to phi(n)/2) Example : n=1783*2879 2x=2564298 and phi(n)=5128596 y=66 a=2564364 We know the value of a ((n+1)/2)-int(sqrt(n)))then it will be easy to find p...

- Sat Aug 20, 2016 8:46 pm UTC
- Forum: Mathematics
- Topic: Goahead52's Math Posts
- Replies:
**148** - Views:
**19028**

### Re: Factorization of odd semi prime is over!

I had sent 2 equations : are they false or true? That is all I want to know. Sharing results is not prohibited by any law. I`m not kid and I know what it means to send a solution for problem as hard as factoring huge numbers. All the secret services will try to kill you or to abduct you. I know that...

- Sat Aug 20, 2016 6:22 pm UTC
- Forum: Mathematics
- Topic: Goahead52's Math Posts
- Replies:
**148** - Views:
**19028**

### Re: Factorization of odd semi prime is over!

lorb wrote:Try those numbers: https://en.wikipedia.org/wiki/RSA_numbers

I know the RSA numbers and challenge so do not send what is known to anyone.

Focus on what I said first.

You will surely find flaws. I know it.

There are 2 main equations.

Are they false or true?

- Sat Aug 20, 2016 2:59 pm UTC
- Forum: Mathematics
- Topic: Goahead52's Math Posts
- Replies:
**148** - Views:
**19028**

### Re: Factorization of odd semi prime is over!

Sorry I forget to mention that q>p.

I have in mind the RSA cryptographic saystem.

For p^2 I have a different equation.

Anyway confirm it or infirm it.

I`m waiting for your useful comments.

I have in mind the RSA cryptographic saystem.

For p^2 I have a different equation.

Anyway confirm it or infirm it.

I`m waiting for your useful comments.

- Sat Aug 20, 2016 1:41 pm UTC
- Forum: Mathematics
- Topic: Goahead52's Math Posts
- Replies:
**148** - Views:
**19028**

### Factorization of odd semi prime is over!

The factorization of odd semi prime is over and could be reduced to a simple linear congruence equation : Here is the solution of an amateur : p and q are odd semi prime We start by this equation which is true : pq*(p-1)(q-1)mod(pq-2)=(p-2)(q-2) This equation is based on some properties of Eulerian ...

- Fri Aug 19, 2016 3:05 pm UTC
- Forum: Logic Puzzles
- Topic: Factorial puzzle
- Replies:
**6** - Views:
**3813**

### Re: Factorial puzzle

I know that phi is multiplicative. I was working on Eulerian Factorial Numbers (EFN) to represent any factorial as product of 2 EFN. The EFN are new kind of numbers with many properties. An EFN is of the form n*phi(n) where phi is the Euler totient. If you mutiply 2 EFN you will obtain an other EFN....

- Thu Aug 18, 2016 10:03 am UTC
- Forum: Mathematics
- Topic: Goahead52's Math Posts
- Replies:
**148** - Views:
**19028**

### Re: New Theorem (prime numbers)?

Thank you all.

I`m not in good health not able to focus on anything. So I will stop posting

Very sorry for bothering you.

Good luck to everybody.

I`m not in good health not able to focus on anything. So I will stop posting

Very sorry for bothering you.

Good luck to everybody.

- Wed Aug 17, 2016 11:13 pm UTC
- Forum: Mathematics
- Topic: Goahead52's Math Posts
- Replies:
**148** - Views:
**19028**

### Re: New Theorem (prime numbers)?

Thank you very much for your comment. If you except n=1 your statement is stronger than mine. I did not check the value where n*phi(n)=1 because I was looking for something else. I have to restate and enlarge my claim to the other prime. I will do it until no one has any comment to add. I checked yo...

- Wed Aug 17, 2016 5:25 pm UTC
- Forum: Mathematics
- Topic: Goahead52's Math Posts
- Replies:
**148** - Views:
**19028**

### Re: New Theorem (prime numbers)?

I have an explanation not a proof. If n is composite with mu(n)=-1 then it has to be square-free and product of an odd number of factors (3,5,7...). If we multiply this number n by its Euler totient we will the product of 3,5,7.... even factors. Hence mu(n*phi(n))=0 (not square free) On the contrary...

- Wed Aug 17, 2016 2:00 pm UTC
- Forum: Mathematics
- Topic: Goahead52's Math Posts
- Replies:
**148** - Views:
**19028**

### New Theorem (prime numbers)?

Let us note F(n)=n*phi(n) where phi () is the Euler totient n positive integer > 0 Theorem : If mu(F(n))=-1 then n is prime (m() is the Mobius function) Check it or find a counterexample. Here is the list of the first few prime : 2,7,11,23,47,59,83,107,167,179,211,227,263,331,347,359,383,463,467,479...

- Wed Aug 17, 2016 1:15 pm UTC
- Forum: Logic Puzzles
- Topic: Factorial puzzle
- Replies:
**6** - Views:
**3813**

### Re: Factorial puzzle

Here is my theorem : Let us call a number of form n*phi(n) an eulerian factorial number EFN (n positive integer > 0). If mu(EFN)=-1 then n is prime (mu() is the Mobius function) n=7 phi(7)=6 EFN(7)=7*6=42 mu(42)=-1 imply that 7 is prime n=11 EFN(11)=110 mu(110)=-1 imply that 11 is prime The converse...

- Wed Aug 17, 2016 12:58 pm UTC
- Forum: Mathematics
- Topic: Goahead52's Math Posts
- Replies:
**148** - Views:
**19028**

### Re: Primes, sequences and infinite

While working on the "Factorial puzzle" posted on Puzzles here I discovered an identical sequence (OEIS A088179) computed based on the Mobius function.

I will post it on the factorial puzzle post.

Amazing surprise with a theorem I have to prove.

I will post it on the factorial puzzle post.

Amazing surprise with a theorem I have to prove.

- Tue Aug 16, 2016 7:04 pm UTC
- Forum: Logic Puzzles
- Topic: Factorial puzzle
- Replies:
**6** - Views:
**3813**

### Factorial puzzle

k!=m*phi(m)*n*phi(n)

k,m,n positive integers

phi is the Euler totient

Find the triplets (k,m,n) such as the equation above holds.

Examples :

k=7

m=5

n=21

or

m=7

n=15

(7,5,21) and (7,7,15) are solutions

k=8

(8,20,21) is solution

Do all the factorials have at least one solution?

k,m,n positive integers

phi is the Euler totient

Find the triplets (k,m,n) such as the equation above holds.

Examples :

k=7

m=5

n=21

or

m=7

n=15

(7,5,21) and (7,7,15) are solutions

k=8

(8,20,21) is solution

Do all the factorials have at least one solution?

- Tue Aug 16, 2016 1:45 pm UTC
- Forum: Mathematics
- Topic: Goahead52's Math Posts
- Replies:
**148** - Views:
**19028**

### Re: Primes, sequences and infinite

I have another one about Combinatorics but I did not find it for now.

My archives are not classified. Only my memory will allow me to find it.

Some are on my second computer.

My archives are not classified. Only my memory will allow me to find it.

Some are on my second computer.

- Tue Aug 16, 2016 1:42 pm UTC
- Forum: Mathematics
- Topic: Goahead52's Math Posts
- Replies:
**148** - Views:
**19028**

### Re: Primes, sequences and infinite

The main idea behind those computation is to find an easily computable sequence U(n) such as : - when n exceed what is yet known (exact values of pi(n) obtained by sieving or any other mean) U(n) will be exactly equal to pi(n) and will stay equal to the infinite. - we know exactly for which value o...

- Tue Aug 16, 2016 12:16 pm UTC
- Forum: Logic Puzzles
- Topic: Sharing secret information publicly
- Replies:
**27** - Views:
**7070**

### Re: Sharing secret information publicly

You are right.

I was totally wrong.

No one to blame other than me.

I was totally wrong.

No one to blame other than me.

- Tue Aug 16, 2016 1:29 am UTC
- Forum: Logic Puzzles
- Topic: Sharing secret information publicly
- Replies:
**27** - Views:
**7070**

### Re: Sharing secret information publicly

There is an easy solution : A will write down 5 cards containing his 3 cards + 2 picked randomly among the remaining 4 B will write down 5 cards containing his 3 cards + 2 chosen depending on his hand and A`s hand Both A and B will know which card C holds without saying C holds card "x" C ...

- Mon Aug 15, 2016 8:42 pm UTC
- Forum: Mathematics
- Topic: Goahead52's Math Posts
- Replies:
**148** - Views:
**19028**

### Re: Primes, sequences and infinite

The main idea behind those computation is to find an easily computable sequence U(n) such as : - when n exceed what is yet known (exact values of pi(n) obtained by sieving or any other mean) U(n) will be exactly equal to pi(n) and will stay equal to the infinite. - we know exactly for which value of...

- Mon Aug 15, 2016 7:12 pm UTC
- Forum: Mathematics
- Topic: Goahead52's Math Posts
- Replies:
**148** - Views:
**19028**

### Re: Primes, sequences and infinite

After some computation I reached the conclusion that pi(n) the counting function does need only the first prime numbers to be computed with big precision. Out of n (assuming that n is very large) how many first primes I need to know to have something precise? I still do not know. It needs lot of tes...

- Mon Aug 15, 2016 12:29 pm UTC
- Forum: Mathematics
- Topic: Goahead52's Math Posts
- Replies:
**148** - Views:
**19028**

### Re: Primes, sequences and infinite

A(p)=S(p)*(p-r)

where r and S(p) are real numbers.

Now I need to compute the values of r.

where r and S(p) are real numbers.

Now I need to compute the values of r.

- Mon Aug 15, 2016 12:00 pm UTC
- Forum: Mathematics
- Topic: Goahead52's Math Posts
- Replies:
**148** - Views:
**19028**

### Re: Primes, sequences and infinite

lorb wrote:Oh well. While you are at it, would you mind to proof the Riemann hypothesis too? It's related, and shouldn't be too hard compared to what you are aiming for now.

Do not worry. Selling roasted almonds to toothless people is much harder than solving Riemann hypothesis.