The tutor continues his discussion about Pythagorean triples.

Back in my January 7, 2016 post I brought up Pythagorean triples, which are all-integer solutions to

x² + y² = z²

The equation above is based on the familiar

a² + b² = c²

An interesting fact is that Pythagorean triples can be generated from the following formulas, with n odd:

Take, for instance, n as 3. Then we have

x=3

y=(3²-1)/2=(9-1)/2=8/2=4 3(2)/2 + 2/2=4

z=(3²+1)/2=(9+1)/2=10/2=5

which is the familiar 3,4,5 triple.

With n=11, we have

x=11

y=(11²-1)/2=(120)/2=60

z=(11²+1)/2=(122)/2=61

Checking, we start with

11²+60²=61²

Squaring, we get

121+3600=3721✓

I’ll be giving more coverage to Pythagorean triples in coming posts:)

Source:

Dudley, Underwood. Elementary Number Theory. New York:
  W H Freeman and Company, 1978.

Jack of Oracle Tutoring by Jack and Diane, Campbell River, BC.