**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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