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PAGE: 626 | SET: Exercises | PROBLEM: 37 |

Statement : is divisible by
.
The statement is False.
Proof :
Let be the statement
is divisible by
.
is the statement that
is divisible by
,
is true since
which is divisible by .
Assume is true where
is a positive integer and we have to prove that
must be
true i.e., show that for some integer
implies that
is divisible by
.
Plug in differerent values :
For :
which is not divisible by
but divisible by
.
For :
which is divisible by
.
For :
which is not divisible by
but divisible by
.
Therefore, is divisible by
only when
is an odd number.
The expression is not divisible by
.

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