Solve this (Inspired by Mehul Arora's comment)

Number Theory Level 3

If a b c ≠ 0 abc\neq{0} and a , b , c ∈ Z + a,b,c\in { Z }^{ + } . Find the no. of ordered pair for ( a , b , c ) (a,b,c) for:

a 2015 + b 2015 = c 2015 a^{2015}+b^{2015}=c^{2015}


The answer is 0.

Department 8 by Department 8 , 27, Israel

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1 solution

Nihar Mahajan
Sep 8, 2015

By Fermat's Last Theorem , no such a , b , c ∈ Z + a,b,c \in \mathbb{Z}^+ and a b c ≠ 0 abc\neq 0 exist satisfying a n + b n = c n ∀ n > 2 a^n+b^n=c^n \ \forall \ n >2 .

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