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Problem 259

Number theory Difficulty 2.2 Multiple choice CEMC Fermat · Canada · 2025

The current calendar year, $2025$ , is a perfect square. In $n$ years from 2025, the calendar year will
again be a perfect square. The smallest possible value of $n$ is

Pick one

Official solutions — 2

Solution 1

Since $\sqrt{2025}=45$ , the
next largest perfect square greater than 2025 is $46^2=2116$ .

Thus, the smallest possible value of $n$ is $2116-2025=91$ .

Solution 2

Since $\sqrt{2025}=45$ , the
next largest perfect square greater than 2025 is $46^2=2116$ .

Thus, the smallest possible value of $n$ is $2116-2025=91$ .

Source: CEMC, University of Waterloo, licensed CC-BY-NC-4.0. Statement reproduced verbatim; metadata (topic, difficulty, ordering) added by this project.