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Topic: A quicker way?
Replies: 8   Last Post: Feb 4, 2013 1:44 PM

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Posts: 12,067
Registered: 7/15/05
Re: A quicker way?
Posted: Feb 4, 2013 10:27 AM
  Click to see the message monospaced in plain text Plain Text   Click to reply to this topic Reply wrote:

>Let n^2 = N + a^2, where n, N and a are integers.
>Knowing N, it is of course possible to find n by trying
> a = 1, 2, 3, 4, etc...
>But doesn't exist a quicker way ?

if you rewrite the equation in the form

(n - a)(n + a) = N

then for each pair of integers u,v with u*v = N, you can
solve the equations

n - a = u
n + a = v

for n and a.


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