Pythagorean triple is (a,b,c) satisfies

Find all Pythagorean triple in (a,a+1,c)

the first two are (3,4,5) and (20,21,29)

thanks!!!

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- Mar 22nd 2009, 06:14 PMchipaiPythagorean triple in (a,a+1,c)
Pythagorean triple is (a,b,c) satisfies

Find all Pythagorean triple in (a,a+1,c)

the first two are (3,4,5) and (20,21,29)

thanks!!! - Mar 22nd 2009, 06:47 PMPaulRS
We require:

Expand:

Now multiply by 2:

So: and note that:

We have:

Set and

So our condition turns into:

And this is a Pell Type equation ! (Read here, if you have any doubts, ask (Nod) ) :) - Mar 22nd 2009, 08:12 PMSoroban
Hello, chipai!

Quote:

Pythagorean triple is satisfies

Find all Pythagorean triple of the form:

The first two are and .

. .

The recursive formulas are:

. .