Square of an Odd number
Number Theory
Level
2
The square of an odd number is always
Odd.
Prime.
None of the above.
Even.
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Any odd number can be written in the form 2n + 1 where n is any integer. So the square of an odd number is nothing but (2n + 1)* ( 2n + 1) = 4n*n + 4n + 1 = 4n(n+1) + 1.
The first term 4n(n+1) in the resulting expression is defenitely even, when 1 is added to an even number it results in an odd number.