Pythagorean triplets have a property that they can be expressed in the form of m^{2}n^{2}, 2mn, m^{2}+n^{2} (where m>n). I have the following questions 
Does 2mn>m^{2}n^{2} always hold?
Do m,n belong to natural numbers?
Thanks in advance.
Question regarding pythagorean triplets
Re: Question regarding pythagorean triplets
No, consider m=6, n=1.nisargshah95 wrote:Pythagorean triplets have a property that they can be expressed in the form of m^{2}n^{2}, 2mn, m^{2}+n^{2} (where m>n). I have the following questions 
Does 2mn>m^{2}n^{2} always hold?
Yes.nisargshah95 wrote:Do m,n belong to natural numbers?

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Re: Question regarding pythagorean triplets
It also true that m^{2}+n^{2} is always greater than the other two?
Re: Question regarding pythagorean triplets
Yes since it's the hypotenuse.nisargshah95 wrote:It also true that m^{2}+n^{2} is always greater than the other two?
The hypotenuse is the largest since c^{2} = a^{2} + b^{2} > a^{2}, b^{2}.