Mock AIME 5 2005-2006 Problems/Problem 5

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Problem

Find the largest prime divisor of $25^2+72^2$.

Solution

$25^2+72^2=5^4+4\cdot 6^4$, and we can use the Sophie Germain Identity on that to get

\[25^2+72^2=(5^2+2\cdot 6^2+2\cdot 5\cdot 6)(5^2+2\cdot 6^2-2\cdot 5\cdot 6)=157\cdot 37\].

$\boxed{157}$ is the largest prime factor of that.

See also

Mock AIME 5 2005-2006 (Problems, Source)
Preceded by
Problem 4
Followed by
Problem 6
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