2011 UNCO Math Contest II Problems/Problem 8
Problem
The integer 
can be expressed as a sum of two squares as 
.
(a) Express 
as the sum of two squares.
(b) Express the product 
as the sum of two squares.
(c) Prove that the product of two sums of two squares, 
, can be represented
as the sum of two squares.
Solution
(a) By testing the perfect squares up to , you can see that 
.
\begin{align*}
\text{ }
\end{align*}
(b) 
.
See Also
| 2011 UNCO Math Contest II (Problems • Answer Key • Resources) | ||
| Preceded by Problem 7 |
Followed by Problem 9 | |
| 1 • 2 • 3 • 4 • 5 • 6 • 7 • 8 • 9 • 10 | ||
| All UNCO Math Contest Problems and Solutions | ||
