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decimal palindrome

Source: Germany Federal - Bundeswettbewerb Mathematik 2009, round 1, p4

April 9, 2020
number theorypalindromesmultiple

Problem Statement

A positive integer is called decimal palindrome if its decimal representation zn...z0z_n...z_0 with zn≠0z_n\ne 0 is mirror symmetric, i.e. if zk=zn−kz_k = z_{n-k} applies to all k=0,...,nk= 0, ..., n. Show that each integer that is not divisible by 1010 has a positive multiple, which is a decimal palindrome.
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