Prove that there is no rational number whose square is 2
Let
be a rational number whose square is 2, where we assume that
is in lowest terms, i.e.
and
have no common integer factors except
(integers relatively prime).
Then
,
and …
Prove that the square of any odd integer is odd
Any odd integer has the form
.
Since,
is 1 more than the even integer
.
The result follows.
Dịch
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