MathDB

P6

Part of 2023 Irish Math Olympiad

Problems(1)

Sum of digits is a square

Source: Irish Mathematical Olympiad 2023 Problem 6

5/14/2023
A positive integer is totally square is the sum of its digits (written in base 1010) is a square number. For example, 1313 is totally square because 1+3=221 + 3 = 2^2, but 1616 is not totally square.
Show that there are infinitely many positive integers that are not the sum of two totally square integers.
number theory