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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
1 • 2 • 3 • 4 • 5 • 6 • 7 • 8 • 9 • 10 • 11 • 12 • 13 • 14 • 15

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Category: Intermediate Algebra Problems

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