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# How to find the 3 Pythagorean triplets with only one number?

**Given:** Pythagorean triplets

**To explain:** Here we have to explain how to find Pythagorean triplets with only one number.

**Solution:**

__
If the number is odd__:

Square the number (n) and then divide it by 2.

Take the integer that is immediately before and after that number

i.e. $\left(\frac{n^{2}}{2} \ -\ 0.5\right)$ and $\left(\frac{n^{2}}{2} \ +\ 0.5\right)$.

Pythagorean triplet = n, $\left(\frac{n^{2}}{2} \ -\ 0.5\right)$ and $\left(\frac{n^{2}}{2} \ +\ 0.5\right)$.

__Example__:

Take number n = 3.

On squaring the number, we get 9.

Now take half of it: $\frac{9}{2}$ = 4.5

The integer immediately before 4.5 = 4

The integer immediately after 4.5 = 5

Therefore, the triplets are 3, 4 and 5.

__
If the number is even__:

Take the half of that number (n) and then square it.

Pythagorean triplet = n, $\left(\frac{n}{2}\right)^{2} \ -\ 1$ and $\left(\frac{n}{2}\right)^{2} \ +\ 1$ *
*

__Example__:

Take number n = 8

Half of n = 4.

Pythagorean triplet = 8, (4^{2 }$-$ 1) and (4^{2} $+$ 1) = 8, 15 and 17.

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