Let

Then

is an integer when is a factor of

So all triples can be expressed as

with

for example,

k = 1 ….. , ,

k = 2 ….. , ,

k = 3 ….. , ,

k = 4 ….. , ,

k = 5 ….. , ,

k = 6 ….. , ,

k = 7 ….. , ,

…………………….

with and

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The following formulas also give all solutions :

$b=tx(x+y), c=ty(x+y), a=txy$, where $t,x,y$ – arbitrary integer numbers.

True