# If a and are any odd integers, then a^{2} + b^{2} is even. Prove?

If a and are any odd integers, then is even.
Prove?
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Proof:
Let two odd positive numbers be where j and k are integers.

where, are integers. Then,

which is even by definition.
where, is also an integer.
Hence, if a and b are any odd integers then is even.
Conclusion:
The statement, "If a and b are any odd integers, then is even" is proved.

Jeffrey Jordon