MathDB

Divisibility on 2 numbers with same amount of digits.

Source: Olimpiada Rioplatense 2013 Level 3, Problem 5.

August 7, 2014

number theorygreatest common divisormodular arithmeticalgorithmnumber theory proposed

Problem Statement

Find all positive integers

n

for which there exist two distinct numbers of

n

digits,

\overline{a_1a_2\ldots a_n}

and

\overline{b_1b_2\ldots b_n}

, such that the number of

2n

digits

\overline{a_1a_2\ldots a_nb_1b_2\ldots b_n}

is divisible by

\overline{b_1b_2\ldots b_na_1a_2\ldots a_n}