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on the set of all positive integers whose all digits are 1,2

Source: 2007 Korean MO, 2nd Round, A.M.

August 18, 2007

modular arithmeticinductionnumber theory unsolvednumber theory

Problem Statement

Let

S

be the set of all positive integers whose all digits are

1

2

. Denote

T_{n}

as the set of all integers which is divisible by

n

, then find all positive integers

n

such that

S\cap T_{n}

is an infinite set.