Is there any theorem to tell if square of a number can be expressed as sum of squares of two other distinct numbers.

I have one such set. {5 4 3}

5^2 = 4^2 + 3^2

Given a number n how to find if the above conditions satisfy ?


closed as unclear what you're asking by Will Jagy, Empty, JonMark Perry, Strants, user91500 Oct 10 '15 at 8:36

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    $\begingroup$ is there some sort of recent contest going on, possibly in programming? This question has been repeated by different people for several days $\endgroup$ – Will Jagy Oct 9 '15 at 23:29
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    $\begingroup$ So how much are you going to win if we give away secrets about famous trios of numbers named after Greek philosophers who were averse to beans? (And how do we get our cut?) $\endgroup$ – Rob Arthan Oct 9 '15 at 23:41
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    $\begingroup$ @RobArthan, not as widely known, the playwright Aeschylus died when an eagle dropped a tortoise on his head. It's in Pliny the Elder. Book 10, Chapter 3, if the link does not quite work. perseus.tufts.edu/hopper/… $\endgroup$ – Will Jagy Oct 9 '15 at 23:56
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    $\begingroup$ The question has been asked frequently lately. A search will find the answer, possibly in a comment. $\endgroup$ – André Nicolas Oct 9 '15 at 23:58
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    $\begingroup$ @WillJagy: did Aeschylus contribute anything to mathematics? (Other than the eagle/tortoise/death statistic)? $\endgroup$ – Rob Arthan Oct 10 '15 at 0:02

There is the concept of Pythagorean Triples. for:


you can use the following values for a,b and c where m and n are any two positive integers such that $m>n$:

$$a^2=m^2-n^2 \; and \; b=2mn\; and \; c^2=m^2+n^2 $$

Here is a sample:

enter image description here

You can read more about the subject in wiki-Pythagorean_triple and for a better method to generate the numbers in here: A Direct Method To Generate Pythagorean Triples .


These sets are called pythagorean triplets for obvious reasons. If {x, y, z} are p. triplets so are any {nx, ny, nz}. If m is odd there's a way to construct a triplet that I'm holding off on sharing but I'll tell you two of the terms are consecutive.


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