Question 190612: # 3. Find a counterexample to the statement "The sum of two squares is an even number"
Answer by jim_thompson5910(35256)   (Show Source):
You can put this solution on YOUR website! # 3
Q: Find a counterexample to the statement "The sum of two squares is an even number"
A:
There are many examples to choose from, but the main thing we need to do is make one of the perfect squares an odd number and the other an even number.
So the list of the first few perfect squares is: 1, 4, 9, 16, 25, 36, 49, 64, 81, 100, etc...
If we select the first two perfect squares and add them, we get  which is NOT even
Or, we could add the numbers 4 and 9 to get  which is NOT even
Or, we could add the numbers 9 and 16 to get  which is NOT even
etc...
So these examples (and you only need one) show that the statement "The sum of two squares is an even number" is false.
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