MathDB

4

Part of 2013 China Northern MO

Problems(1)

13^k=a^2 +b^2

Source: China Northern MO 2013 p4 CNMO

11/25/2022
For positive integers n,a,bn,a,b, if n=a2+b2n=a^2 +b^2, and aa and bb are coprime, then the number pair (a,b)(a,b) is called a square split of nn (the order of a,ba, b does not count). Prove that for any positive kk, there are only two square splits of the integer 13k13^k.
number theorySum of Squares