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UKMT Junior Mathematical Challenge, 2021

Number theory Difficulty 2.0 Junior Find the answer United Kingdom

In 1770, Joseph-Louis Lagrange proved that every positive integer can be written as the sum of four squares. For example, $13 = 0^2 + 0^2 + 2^2 + 3^2$ . How many of the first 15 positive integers can be written as the sum of three squares?

(A) $11$ (B) $12$ (C) $13$ (D) $14$ (E) $15$

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