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Divisibilities on sum of digits

Source: Mexico National Olympiad Mock Exam 2018 Problem 4

November 6, 2018
number theorysum of digitsDivisibility

Problem Statement

For each positive integer nn let s(n)s(n) denote the sum of the decimal digits of nn. Find all pairs of positive integers (a,b)(a, b) with a>ba > b which simultaneously satisfy the following two conditions
a∣b+s(a)a \mid b + s(a) b∣a+s(b)b \mid a + s(b)
Proposed by Victor Domínguez
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