MathDB
Equation with primes and perfect square

Source: Mexican University Math Olympiad 2024, Problem 1

October 1, 2024
number theoryprime numbersPerfect Squares

Problem Statement

Let x x , y y , p p be positive integers that satisfy the equation x4=p+9y4 x^4 = p + 9y^4 , where p p is a prime number. Show that p2−13 \frac{p^2 - 1}{3} is a perfect square and a multiple of 16.
Back to ProblemsView on AoPS