2014 UMO Problems/Problem 2: Difference between revisions
Created page with "==Problem == (a) Find all positive integers <math>x</math> and <math>y</math> that satisfy <cmath>x^2+y^2 = 2014,</cmath> or prove that there are no solutions. (b) Find all po..." |
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== See Also == | == See Also == | ||
{{UMO box|year=2014|num-b=1|num-a=3}} | {{UMO box|year=2014|num-b=1|num-a=3}} | ||
[[Category:Intermediate Algebra Problems]] | |||
Revision as of 14:29, 14 October 2014
Problem
(a) Find all positive integers 
and 
that satisfy ![\[x^2+y^2 = 2014,\]](http://latex.artofproblemsolving.com/2/5/a/25a3179e00402d5b487e7101b600041bf5ffe906.png)
or prove that there are no solutions.
(b) Find all positive integers and that satisfy ![\[x^2 + y^2 = 3222014,\]](http://latex.artofproblemsolving.com/8/8/c/88cf74cb3ba0d63a5d843c9e2cfb0171dac5fa2f.png)
or prove that there are no
solutions.
Solution
See Also
| 2014 UMO (Problems • Answer Key • Resources) | ||
| Preceded by Problem 1 |
Followed by Problem 3 | |
| 1 • 2 • 3 • 4 • 5 • 6 | ||
| All UMO Problems and Solutions | ||
