Question

Write the Pythagorean triplet whose one of the numbers is 4.

Answer 1

We know that, for any natural number greater than 1, $(2m,m^2-1,m^2+1)$ is a Pythagorean triplet.
So, one number is $2m$, then other two numbers are $m^2+1$ and $m^2-1$
Hence, one number is 4, then pythagorean triplet,
$2m=4\Rightarrow m=2$
$\therefore m^2+1=2^2+1=4+1=5$
and $m^2-1=2^2-1=4-1=3$
Now, $3^2+4^2=5^2$
$\Rightarrow 9+16=25\Rightarrow 25=25$
So 3, 4 and 5 are pythagorean triplets.