MathDB

3-digit palindrome and binary expansion \overline {xyx}

Source: RMM Shortlist 2017 N2

July 4, 2019

number theorypalindromesbinary representation

Problem Statement

Let

x, y

and

k

be three positive integers. Prove that there exist a positive integer

N

and a set of

k + 1

positive integers

\{b_0,b_1, b_2, ... ,b_k\}

, such that, for every

i = 0, 1, ... , k

, the

b_i

-ary expansion of

N

is a

3

-digit palindrome, and the

b_0

-ary expansion is exactly \overline{\mbox{xyx}}.
proposed by Bojan Basic, Serbia