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9 votes
Prove: The square of an even number is even

User Fourcube
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1 Answer

14 votes
14 votes
  • Squares of even numbers are even, and are divisible by 4, since (2n)2 = 4n2. Squares of odd numbers are odd, and are congruent to 1 modulo 8, since (2n + 1)2 = 4n(n + 1) + 1, and n(n + 1) is always even.
User Sameer Joshi
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