MathDB
Prove that this does not have any integer solutions

Source: 2009 Jozsef Wildt International Mathematical Competition

April 15, 2020
number theoryprime numbers

Problem Statement

Let p1p_1, p2p_2 be two odd prime numbers and α\alpha , nn be positive integers with α>1\alpha >1, n>1n>1. Prove that if the equation (p2−12)p1+(p2+12)p1=αn\left (\frac{p_2 -1}{2} \right )^{p_1} + \left (\frac{p_2 +1}{2} \right )^{p_1} = \alpha^n does not have integer solutions for both p1=p2p_1 =p_2 and p1≠p2p_1 \neq p_2.
Back to ProblemsView on AoPS