Find all the positive integers $a{}$ and $b{}$ such that $(7^a-5^b)/8$ is a prime number. Cosmin Manea and Dragoș Petrică
Problem
Source: Romania JBMO TST 2024 Day 1 P1
Tags: number theory, modular arithmetic, prime numbers
Source: Romania JBMO TST 2024 Day 1 P1
Tags: number theory, modular arithmetic, prime numbers
Find all the positive integers $a{}$ and $b{}$ such that $(7^a-5^b)/8$ is a prime number. Cosmin Manea and Dragoș Petrică