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Given the statement, "If 
is odd, then 
is odd," its contrapositive claims that, "If is not odd, then is not odd."
So assume is not odd, i.e. is even. This means there is an integer 
for which 
. Squaring this gives 
.
Well, we can write
, and 
is just another integer, which means 
must be even.
So assume
Well, we can write