Difference between revisions of "1987 AIME Problems/Problem 14"
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== Problem == | == Problem == | ||
Compute | Compute | ||
− | <div style="text-align:center;"><math>\frac{(10^4+324)(22^4+324)(34^4+324)(46^4+324)(58^4+324)}{(4^4+324)(16^4+324)(28^4+324)(40^4+324)(52^4+324)}</math></div> | + | <div style="text-align:center;"><math>\frac{(10^4+324)(22^4+324)(34^4+324)(46^4+324)(58^4+324)}{(4^4+324)(16^4+324)(28^4+324)(40^4+324)(52^4+324)}.</math></div> |
== Solution == | == Solution == |
Revision as of 23:55, 6 March 2015
Problem
Compute
Solution
The Sophie Germain Identity states that can be factorized as . Each of the terms is in the form of . Using Sophie-Germain, we get that .
Almost all of the terms cancel out! We are left with .
See also
1987 AIME (Problems • Answer Key • Resources) | ||
Preceded by Problem 13 |
Followed by Problem 15 | |
1 • 2 • 3 • 4 • 5 • 6 • 7 • 8 • 9 • 10 • 11 • 12 • 13 • 14 • 15 | ||
All AIME Problems and Solutions |
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