Question

What is the Pythagorean Triples using the values, $m=3$ and $n=5$?

Answer 1

Condition for constructing Pythagorean triples:
When m and n are any two positive integers $(m<n)$:

$a=n^2-m^2$

$b=2nm$

$c=n^2+m^2$

Then $a,b$ and $c$ are Pythagorean triple

Here $m=3$ and $n=5$

$\therefore 5^2-3^2$

$\Rightarrow 25-9=16$

$\therefore b=2\times 5\times 3=30$

$\therefore c=5^2+3^2$

$\Rightarrow 25+9=34$

Hence Pythagorean triples are $16,30,34$.