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min n, such that n = (a - 1) mod $a$ for all a \in {2,3,..., 10 }

Source: Netherlands - Dutch NMO 1969 p1

January 31, 2023

number theoryremainder

Problem Statement

Determine the smallest

n

such that

n \equiv (a - 1)

mod

a

for all

a \in \{2,3,..., 10\}