Please prove the following without using outside lemmas,  "Let a, b ∈ Z. Prove that if ab is odd, then a2 + b2 is even."

Operations Research : Applications and Algorithms
4th Edition
ISBN:9780534380588
Author:Wayne L. Winston
Publisher:Wayne L. Winston
Chapter6: Sensitivity Analysis And Duality
Section6.7: The Dual Theorem And Its Consequences
Problem 8P
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Please prove the following without using outside lemmas, 

"Let a, b ∈ Z. Prove that if ab is odd, then a2 + b2 is even."

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