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Is the following a good way to generate primitive pythagorean triples?

```
pythag[n_] := Block[{soln = Solve[{a^2 + b^2 == c^2, c <= n, 0 < a < b < c}, {a, b, c}, Integers]},
{Length[soln], Count[GCD[a, b] == GCD[b, c] == GCD[c, a] == 1 /. soln, True]}
]
```

'And fun? If maths is fun, then getting a tooth extraction is fun. A viral infection is fun. Rabies shots are fun.'

'God exists because Mathematics is consistent, and the devil exists because we cannot prove it'

I'm not crazy, my mother had me tested.

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**anonimnystefy****Real Member**- From: Harlan's World
- Registered: 2011-05-23
- Posts: 16,018

Why not just use Euclid's formula?

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Taking a new step, uttering a new word, is what people fear most. ― Fyodor Dostoyevsky, Crime and Punishment

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I would love to but I do not know how to do that on M.

'And fun? If maths is fun, then getting a tooth extraction is fun. A viral infection is fun. Rabies shots are fun.'

'God exists because Mathematics is consistent, and the devil exists because we cannot prove it'

I'm not crazy, my mother had me tested.

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**bobbym****Administrator**- From: Bumpkinland
- Registered: 2009-04-12
- Posts: 106,408

Here are some I used:

`somepytriples[m_]:={m,((m^2-1)/2),((m^2+1)/2)}`

`morepytriples[u_,v_,r_]:={(u^2-v^2)r,2*u*v*r,(u^2+v^2)r}`

`pytriples[m_,n_]:={n^2-m^2,2m*n,n^2+m^2}`

**In mathematics, you don't understand things. You just get used to them.****If it ain't broke, fix it until it is.****No great discovery was ever made without a bold guess. **

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How do I iterate m and n through ranges?

I have found yet another truly marvelous algorithm.

http://stackoverflow.com/questions/18294496/proof-pythagorean-triple-algorithm-is-faster-by-euclids-formula

The last comment therein

'And fun? If maths is fun, then getting a tooth extraction is fun. A viral infection is fun. Rabies shots are fun.'

'God exists because Mathematics is consistent, and the devil exists because we cannot prove it'

I'm not crazy, my mother had me tested.

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**bobbym****Administrator**- From: Bumpkinland
- Registered: 2009-04-12
- Posts: 106,408

The search will be on for one that can do what you want as soon as you define what you want.

Here is another one courtesy of Chyanog cao:

`Pick[#, (#^2).{1, 1, -1}, 0] &@Subsets[Range[200], {3}]`

For some really fast code you must go to the gurus.

http://mathematica.stackexchange.com/qu … ean-triple

Mr Wizards code, woof!

```
genPTunder[lim_Integer?Positive] :=
Module[{prim},
prim = Join @@
Table[If[
CoprimeQ[m, n], {2 m n, m^2 - n^2, m^2 + n^2}, ## &[]], {m, 2,
Floor@Sqrt@lim}, {n, 1 + m~Mod~2, m, 2}];
Union @@ (Range[lim~Quotient~Max@#]~KroneckerProduct~{Sort@#} & /@
prim)]
genPTunder[200] // Length
```

**In mathematics, you don't understand things. You just get used to them.****If it ain't broke, fix it until it is.****No great discovery was ever made without a bold guess. **

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Who is cao?

I do not get your code.

'God exists because Mathematics is consistent, and the devil exists because we cannot prove it'

I'm not crazy, my mother had me tested.

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**bobbym****Administrator**- From: Bumpkinland
- Registered: 2009-04-12
- Posts: 106,408

That is the guys name.

Neither of those was written by me. RIPOSTP, produced those.

**In mathematics, you don't understand things. You just get used to them.****If it ain't broke, fix it until it is.****No great discovery was ever made without a bold guess. **

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What does compiling Marhematica code mean?

'God exists because Mathematics is consistent, and the devil exists because we cannot prove it'

I'm not crazy, my mother had me tested.

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**bobbym****Administrator**- From: Bumpkinland
- Registered: 2009-04-12
- Posts: 106,408

It means producing superfast pseudocode. Not exactly machine instructions but code that M can execute much faster. M can also be converted into C++ code.

**In mathematics, you don't understand things. You just get used to them.****If it ain't broke, fix it until it is.****No great discovery was ever made without a bold guess. **

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Why would you do that?

'God exists because Mathematics is consistent, and the devil exists because we cannot prove it'

I'm not crazy, my mother had me tested.

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**bobbym****Administrator**- From: Bumpkinland
- Registered: 2009-04-12
- Posts: 106,408

Because code might run dozens of times faster!

**In mathematics, you don't understand things. You just get used to them.****If it ain't broke, fix it until it is.****No great discovery was ever made without a bold guess. **

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How do I figure out which is the triple, not nexessarily primitive, (p,q,r) such that p+q+r is minimised and p>=20

'God exists because Mathematics is consistent, and the devil exists because we cannot prove it'

I'm not crazy, my mother had me tested.

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**bobbym****Administrator**- From: Bumpkinland
- Registered: 2009-04-12
- Posts: 106,408

Did you try to program it?

**In mathematics, you don't understand things. You just get used to them.****If it ain't broke, fix it until it is.****No great discovery was ever made without a bold guess. **

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