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b | (a-1), (2a+1) | (5b-3), a>1

Source: Greece Junior Math Olympiad 2023 p4

March 2, 2024

number theoryDivisorsdivides

Problem Statement

Find all positive integers

a,b

with

a>1

such that,

b

is a divisor of

a-1

and

2a+1

is a divisor of

5b-3

.

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