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a+k divides b+k for all k<b implies a-k|b-k for all k<b

Source: St Petersburg 2022 9.1

September 28, 2022

number theory

Problem Statement

The positive integers

a

and

b

are such that

a+k

is divisible by

b+k

for all positive integers numbers

k<b

. Prove that

a-k

is divisible by

b-k

for all positive integers

k<b