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

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== See Also ==
 
== See Also ==
 
{{UNCO Math Contest box|n=II|year=2011|num-b=7|num-a=9}}
 
{{UNCO Math Contest box|n=II|year=2011|num-b=7|num-a=9}}
 
[[Category:Intermediate Algebra Theory Problems]]
 

Revision as of 20:03, 23 January 2017

Problem

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.


Solution

See Also

2011 UNCO Math Contest II (ProblemsAnswer KeyResources)
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