MathDB

M2671

Part of Kvant 2021

Problems(1)

Roots raised to the p-th power

Source: Kvant Magazine No. 10 2021 M2671

3/9/2023
Let x1x_1 and x2x_2 be the roots of the equation x2−px+1=0x^2-px+1=0 where p>2p>2 is a prime number. Prove that x1p+x2px_1^p+x_2^p is an integer divisible by p2p^2.
From the folklore
algebranumber theoryKvant