2006 UNCO Math Contest II Problems/Problem 9

Problem

Determine three positive integers $a,b$ and $c$ that simultaneously satisfy the following three conditions:

(i) $a<b<c$

(ii) Each of $a+b,a+c$ and $b+c$ is the square of an integer, and

(iii) $c$ is as small as is possible.

$a=6;b=19,c=30$ (also $2-34-47$ )

2006 UNCO Math Contest II (Problems • Answer Key • Resources)
Preceded by Problem 8	Followed by Problem 10
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All UNCO Math Contest Problems and Solutions