The statement is is divisible by .

Condition I:

First show that the above statement is true when .

When , the statement is .

Condition 1 of the Principle of Mathematical Induction holds.

Condition II:

Assume that is divisible by holds for some , and determine whether the formula then holds for .

Assume that, is divisible by for some .

Now need show that,

is divisible by .

It follows that,

Since is divisible by and is divisible by ,  is also divisible by .

Thus, Condition II also holds.

The statement is true for all natural numbers.

The statement is true for all natural numbers.