Difference between revisions of "2021 JMPSC Accuracy Problems/Problem 13"
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+ | ==See also== | ||
+ | #[[2021 JMPSC Sprint Problems|Other 2021 JMPSC Sprint Problems]] | ||
+ | #[[2021 JMPSC Sprint Answer Key|2021 JMPSC Sprint Answer Key]] | ||
+ | #[[JMPSC Problems and Solutions|All JMPSC Problems and Solutions]] | ||
+ | {{JMPSC Notice}} |
Revision as of 16:19, 11 July 2021
Contents
[hide]Problem
Let and be nonnegative integers such that Find the sum of all possible values of
Solution
Notice that since and are both integers, and are also both integers. We can then use casework to determine all possible values of :
Case 1: .
The solutions for and are the roots of , which are not real.
Case 2: .
The solutions for and are the roots of , which are not real.
Case 3: .
The solutions for and are the roots of , which are and .
Case 4:
The solutions for and are the roots of , which are and .
Therefore, the answer is .
~kante314
~Revised and Edited by Mathdreams
Solution 2
Note we are dealing with Pythagorean triples, so , and we have is a member of the set too. We see has work, but has nothing work. If , we have work. The answer is ~Geometry285
See also
The problems on this page are copyrighted by the Junior Mathematicians' Problem Solving Competition.