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
.
(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 |