1993 UNCO Math Contest II Problems/Problem 6

Problem

Observe that $\begin{align*} 2^2+3^2+6^3 &= 7^2 \\ 3^2+4^2+12^3 &= 13^2 \\ 4^2+5^2+20^3 &= 21^2 \\ \end{align*}$

(a) Find integers $x$ and $y$ so that $5^2+6^2+x^2=y^2.$

(b) Conjecture a general rule that is being illustrated here.

(c) Prove your conjecture.

1993 UNCO Math Contest II (Problems • Answer Key • Resources)
Preceded by Problem 5	Followed by Problem 7
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All UNCO Math Contest Problems and Solutions