MathDB
Primes dividing their indices

Source: Mexican Mathematical Olympiad 2013 Problem 1

December 1, 2013
inequalitiesnumber theoryprime numbersnumber theory proposed

Problem Statement

All the prime numbers are written in order, p1=2,p2=3,p3=5,...p_1 = 2, p_2 = 3, p_3 = 5, ... Find all pairs of positive integers aa and bb with a−b≥2a - b \geq 2, such that pa−pbp_a - p_b divides 2(a−b)2(a-b).
Back to ProblemsView on AoPS