Question regarding pythagorean triplets

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

Question regarding pythagorean triplets

Post by nisargshah95 »

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?

Thanks in advance.

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

Re: Question regarding pythagorean triplets

Post by thundre »

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.
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nisargshah95
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Joined: Sat Jan 07, 2012 7:50 pm

Re: Question regarding pythagorean triplets

Post by nisargshah95 »

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

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kevinsogo
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Re: Question regarding pythagorean triplets

Post by kevinsogo »

nisargshah95 wrote:It also true that m2+n2 is always greater than the other two?
Yes since it's the hypotenuse.

The hypotenuse is the largest since c2 = a2 + b2 > a2, b2.

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