Question

The primitive Pythagorean triplet (3, 4, 5) is arguably the most famous and commonly used. Find the parameters m and n used in Euclid's formula to generate this triple.

• A. 2, 1
• B. 1, 3
• C. 2, 2
• D. 1, 1

Answer 1

The correct option is A 2, 1

Lets start with;
$a=3=m^2-n^2$ $\cdots I$
$b=4=2mn$ $\cdots II$
$c=5=m^2+n^2$ $\cdots III$
If we add equation I and II we get;
$a+c=8=2m^2-n^2+n^2$
$=2m^2$
$\therefore \text{/}{8}^4=\text{/}2m^2$
m = 2
and substituting we get,
$n=\frac{4}{2\left(2\right)}=1$
$\therefore$ The parameters m and n are thus 2 and 1 respectively.