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Relatives of a number

Source: Mexican Mathematical Olympiad 2006 Problem 1

September 28, 2014

number theory proposednumber theory

Problem Statement

Let

ab

be a two digit number. A positive integer

n

is a relative of

ab

if:
[*] The units digit of

n

b

. [*] The remaining digits of

n

are nonzero and add up to

a

. Find all two digit numbers which divide all of their relatives.