Difference between revisions of "Mock AIME 5 2005-2006 Problems/Problem 5"
(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== | ==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== | ==Solution== | ||
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==See also== | ==See also== | ||
| + | {{Mock AIME box|year=2005-2006|n=5|source=76847|num-b=4|num-a=6}} | ||
[[Category:Intermediate Algebra Problems]] | [[Category:Intermediate Algebra Problems]] | ||
Latest revision as of 15:23, 2 March 2008
Problem
Find the largest prime divisor of 
.
Solution
, and we can use the Sophie Germain Identity on that to get
![\[25^2+72^2=(5^2+2\cdot 6^2+2\cdot 5\cdot 6)(5^2+2\cdot 6^2-2\cdot 5\cdot 6)=157\cdot 37\]](http://latex.artofproblemsolving.com/d/8/d/d8dbc02ec8c1c15a8a73f65f5ca77aa601fb3d02.png)
.
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 | ||
