## Question regarding pythagorean triplets

Arithmetic, algebra, number theory, sequence and series, analysis, ...
nisargshah95
Posts: 5
Joined: Sat Jan 07, 2012 7:50 pm

### Question regarding pythagorean triplets

Pythagorean triplets have a property that they can be expressed in the form of m2-n2, 2mn, m2+n2 (where m>n). I have the following questions -
Does 2mn>m2-n2 always hold?
Do m,n belong to natural numbers?

thundre
Posts: 356
Joined: Sun Mar 27, 2011 10:01 am

### Re: Question regarding pythagorean triplets

nisargshah95 wrote:Pythagorean triplets have a property that they can be expressed in the form of m2-n2, 2mn, m2+n2 (where m>n). I have the following questions -
Does 2mn>m2-n2 always hold?
No, consider m=6, n=1.
nisargshah95 wrote:Do m,n belong to natural numbers?
Yes.

nisargshah95
Posts: 5
Joined: Sat Jan 07, 2012 7:50 pm

### Re: Question regarding pythagorean triplets

It also true that m2+n2 is always greater than the other two?

kevinsogo