Difference between revisions of "1993 UNCO Math Contest II Problems/Problem 6"
(Created page with "== Problem == Observe that <cmath>\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*}</cmath> (a) Find integers <math>x</math> a...") |
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| Line 4: | Line 4: | ||
Observe that | Observe that | ||
<cmath>\begin{align*} | <cmath>\begin{align*} | ||
| − | 2^2+3^2+6^ | + | 2^2+3^2+6^2 &= 7^2 \\ |
| − | 3^2+4^2+12^ | + | 3^2+4^2+12^2 &= 13^2 \\ |
| − | 4^2+5^2+20^ | + | 4^2+5^2+20^2 &= 21^2 \\ |
\end{align*}</cmath> | \end{align*}</cmath> | ||
| Line 14: | Line 14: | ||
(c) Prove your conjecture. | (c) Prove your conjecture. | ||
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== Solution == | == Solution == | ||
Revision as of 14:39, 20 October 2014
Problem
Observe that
(a) Find integers 
and 
so that 
(b) Conjecture a general rule that is being illustrated here.
(c) Prove your conjecture.
Solution
See also
| 1993 UNCO Math Contest II (Problems • Answer Key • Resources) | ||
| Preceded by Problem 5 |
Followed by Problem 7 | |
| 1 • 2 • 3 • 4 • 5 • 6 • 7 • 8 • 9 • 10 | ||
| All UNCO Math Contest Problems and Solutions | ||
