> > > "a^2 + b^2 = c^2 + 1".
> >
> spike Jones wrote: > By inspection this has infinitely many solutions.
Dan Fabulich wrote:
> But *which* solutions? Can you come up with a function for a, b and c
> such that they'll always satisfy this equation?
Sure: a = +/-1, b = +/- c,
or: b = +/-1, a = +/- c
Here are some examples of solutions to a^2 + b^2 = c^2 + 1:
a b c
1 2 -2
-1 -3 3
4 -1 - 4
-1 5 -5
-6 1 6
1 7 7
+/-1 +/-n +/-n
+/-n +/-1 +/-n
where n is any integer.
> That's what's meant by a "solution" here.
Dan, perhaps Ive misunderstood the question? spike
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