MathDB
2023 Fall LMT Team #4 positive two-digit number

Source:

February 4, 2024
number theory

Problem Statement

Fred chooses a positive two-digit number with distinct nonzero digits. Laura takes Fred’s number and swaps its digits. She notices that the sum of her number and Fred’s number is a perfect square and the positive difference between them is a perfect cube. Find the greater of the two numbers.