Difference between revisions of "Mock AIME 5 2005-2006 Problems/Problem 5"

Latest revision as of 16:23, 2 March 2008

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

$25^2+72^2=5^4+4\cdot 6^4$ , 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.

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 ==Problem==
-Find the largest prime divisor of <math>25^2+72^2</math>.
+Find the largest [[prime]] [[divisor]] of <math>25^2+72^2</math>.
 ==Solution==