AoPSWiki
Looking for a challenging algebra text? Preparing for MATHCOUNTS or the AMC exams?
Check out Art of Problem Solving's Introduction to Algebra by Richard Rusczyk.

Mock AIME 5 2005-2006 Problems/Problem 5

From AoPSWiki

Revision as of 20:23, 2 March 2008 by 1=2 (Talk | contribs)
(diff) ← Older revision | Current revision (diff) | Newer revision → (diff)

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
Retrieved from "http://www.artofproblemsolving.com/Wiki/index.php/Mock_AIME_5_2005-2006_Problems/Problem_5"
Looking for a challenging algebra text? Preparing for MATHCOUNTS or the AMC exams?
Check out Art of Problem Solving's Introduction to Algebra by Richard Rusczyk.
© Copyright 2008 AoPS Incorporated. All Rights Reserved. • Foundation • Privacy • Contact Us