Question

Write a Pythagorean triplet whose smallest number is 8

Answer 1

We can get Pythagorean triplets by using general form $2m,m^2-1,m^2+1$
Let $m^2-1=8$
So $m^2=8+1=9$
Which gives m = 3
Therefore, 2m = 6 and $m^2+1=10$
The triplet we get 6, 8, 10 but 8 is not the smallest number.
Now let 2m = 8
Therefore, $m^2-1=16-1=15$
$m^2+16+1=17$
the triple is 8, 15, 17 with 8 as the smallest number.