Difference between revisions of "2011 UNCO Math Contest II Problems/Problem 8"

Revision as of 02:22, 13 January 2019

The integer $45$ can be expressed as a sum of two squares as $45 = 3^2 + 6^2$ .

(a) Express $74$ as the sum of two squares.

(b) Express the product $45\cdot 74$ as the sum of two squares.

(c) Prove that the product of two sums of two squares, $(a^2+b^2)(c^2+d^2)$ , can be represented as the sum of two squares.

(a) $74$ (b) $45 \times 74$

@@ Line 13: / Line 13: @@
 == Solution ==
+(a) <math>74</math> (b) <math>45 \times 74</math>
 == See Also ==
 {{UNCO Math Contest box|n=II|year=2011|num-b=7|num-a=9}}

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