Let n satisfy the equation, a^n+b^n=c^2. When a,b,c are prime numbers and n is an integer, there is one solution at least for the equation.

How to find the biggest possible value of n?

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- Jul 11th 2012, 07:18 AMMhmh96Finding the biggest possible value of n
Let n satisfy the equation, a^n+b^n=c^2. When a,b,c are prime numbers and n is an integer, there is one solution at least for the equation.

How to find the biggest possible value of n? - Jul 11th 2012, 10:13 AMa tutorRe: Finding the biggest possible value of n
Could you give us the solution that you say exists?

Have you managed to narrow down the possibilities for a and b?

I have made some progress but have not found a solution. - Jul 11th 2012, 10:56 AMMhmh96Re: Finding the biggest possible value of n
I think i solved it

http://store2.up-00.com/June12/AOm33041.jpg

And take Mod 5 in the last equation - Jul 11th 2012, 01:02 PMa tutorRe: Finding the biggest possible value of n
- Jul 11th 2012, 02:33 PMa tutorRe: Finding the biggest possible value of n
How about 2+2=4? :p

- Jul 11th 2012, 02:52 PMrichard1234Re: Finding the biggest possible value of n
It's really easy to show that one of a,b must be 2.

Then use casework on the parity of n. Note that if n is odd, the LHS factors.