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11... 11 x 11... 11 is palindrome

Source: Switzerland - 2009 Swiss MO Final Round p2

December 26, 2022
number theoryDigits

Problem Statement

A palindrome is a natural number that works in the decimal system forwards and backwards read is the same size (e.g. 11292111129211 or 73377337). Determine all pairs (m,n)(m, n) of natural numbers, such that (11...11⏟m)⋅(11...11⏟n)(\underbrace{11... 11}_{m}) \cdot (\underbrace{11... 11}_{n}) is a palindrome.
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