MathDB

5.

Part of 2023 Polish Junior Math Olympiad Finals

Problems(1)

Digits and divisibility

Source: 2023 Polish Junior Mathematical Olympiad Finals

5/5/2023
Find all pairs of positive integers mm, nn such that the (m+n)(m+n)-digit number 33…3⏟m66…6⏟n\underbrace{33\ldots3}_{m}\underbrace{66\ldots 6}_{n} is a perfect square.
number theory