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Source: Ukrainian Mathematical Olympiad 2024. Day 2, Problem 8.7

March 20, 2024
number theory

Problem Statement

Prove that there exist infinitely many positive integers that can't be represented in form abcāˆ’bada^{bc} - b^{ad}, where a,b,c,da, b, c, d are positive integers and a,b>1a, b>1.
Proposed by Anton Trygub, Oleksii Masalitin
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