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number n is a d-digit palindrome in all number bases b_1,b_2,..., b_K

Source: Balkan BMO Shortlist 2016 C1

July 30, 2019
palindromesnumber theorynumber base

Problem Statement

Let positive integers KK and dd be given. Prove that there exists a positive integer nn and a sequence of KK positive integers b1,b2,...,bKb_1,b_2,..., b_K such that the number nn is a dd-digit palindrome in all number bases b1,b2,...,bKb_1,b_2,..., b_K.
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