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HMMT February Guts Round, 2024

Number theory Difficulty 4.7 AIME Prove it United States

Problem:

Compute the sum of all integers $n$ such that $n^{2}-3000$ is a perfect square.

Solution

Solution:

If $n^{2}-3000$ is a square, then $(-n)^{2}-3000$ is also a square, so the sum is 0.

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Source: MathNet, licensed CC-BY-4.0. Statement reproduced verbatim; metadata (topic, difficulty) added by this project.