Mock AIME 5 2005-2006 Problems/Problem 5

Revision as of 15:58, 13 February 2008 by 1=2 (talk | contribs) (New page: ==Problem== Find the largest prime divisor of <math>25^2+72^2</math>. ==Solution== <math>25^2+72^2=5^4+4\cdot 6^4</math>, and we can use the Sophie Germain Identity on that to get <...)
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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