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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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.
I think i solved it And take Mod 5 in the last equation
Originally Posted by Mhmh96 I think i solved it What's your solution? Originally Posted by Mhmh96 And take Mod 5 in the last equation Why?
How about 2+2=4?
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.
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