MathDB
Squares consisting of digits 0, 4, 9

Source: Bulgaria MO Regional round 2024, 9.3

February 13, 2024
number theory

Problem Statement

A positive integer nn is called a <spanclass=′latex−italic′>supersquare</span><span class='latex-italic'>supersquare</span> if there exists a positive integer mm, such that 10∤m10 \nmid m and the decimal representation of n=m2n=m^2 consists only of digits among {0,4,9}\{0, 4, 9\}. Are there infinitely many <spanclass=′latex−italic′>supersquares</span><span class='latex-italic'>supersquares</span>?
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