8

Part of 2021 Middle European Mathematical Olympiad

Problems(1)

Perfect squares in base 4 with only digits 1 and 2

Source: 2021 MEMO T-8

Prove that there are infinitely many positive integers

n

n^2

written in base

4

contains only digits

1

2

number theoryDigitsPerfect SquaresmemoMEMO 2021