Question

What is the Pythagorean Triples using the values, $m=1$ 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 $m=1$ and $n=5$

$\therefore 5^2-1^2$

$\Rightarrow 25-1=24$

$\therefore b=2\times 5\times 1=10$

$\therefore c=5^2+1^2$

$\Rightarrow 25+1=26$

Hence Pythagorean triples are $24,10,26$.