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$$5*5=3*3+4*4$$

Integers a,b,c
For a=1 to 100
For b=1 to 100
For c=1 to 100
if c*c=a*a+b*b
list a.b,c
Next c
Next b
Next a

I am 74.

I am interested in youth-hood practical mathematics. Child can use strings of 3,4,5 to draw a right-angled triangle. This 3,4,5 triangle also shows a short-cut 5,saves 3+4 by 2. I come across this site by chance. I even forget the Language I used some 50 years ago. I would be very much obliged to be enlighted on this question.

Matthew Leingang
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wengweng weng
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  • There is a simple formula that gives all solutions to $a^2+b^2=c^2$: $a=2kmn$, $b=k(m^2-n^2)$, $c=k(m^2+n^2)$, $m,n,k$ arbitrary integers. Or type "pythagorean triples" into the web, I'm sure you'll find that someone has tabulated everything you want. – Gerry Myerson Jun 20 '18 at 12:40
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    Wikipedia's "Pythagorean triple" entry lists "primitive" triples with $c \leq 300$. ("Primitive" triples have no common factors.) – Blue Jun 20 '18 at 12:40
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    Hi, welcome. Most of our new users are students looking for homework answers. It's nice to hear from adults still curious about learning and sharing mathematics. – Matthew Leingang Jun 20 '18 at 12:45

1 Answers1

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You are asking for what are called "Pythagorean triples": sets of integers satisfying $a^2+b^2=c^2$. There is a formula for generating all such sets of integers, and you can read all about it in the Wikipedia article: Pythagorean triple.

Near the top of that article is a list which is almost precisely what you are looking for. The only difference is this: if we have a triple such as $(3,4,5)$, you can obtain others by multiplying all three numbers by the same factor, i.e., we have $(6,8,10)$, $(9,12,15)$, etc. These multiples are not included in the list at Wikipedia (they are not what we call "primitive"), but you can find them all without too much work.

G Tony Jacobs
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