Let There exists such that , where .

First we will show that P(1) and P(2) are true.

There exists such that .

satisfies the equation and hence P(1) is true.

There exists such that .

satisfies the equation and hence P(2) is true.

Strong Induction Hypothesis: The proposition is true for all

We will show that is true.

By strong induction hypothesis, is true. This means there exists such that . Multiply the equation by to get . So the integer triple satisfies

Hence is true.

Observe that I have proved and initially.

Question:Is it sufficient to prove P(1)alone?