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

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quasi

Posts: 10,315
Registered: 7/15/05
Re: A quicker way?
Posted: Feb 4, 2013 10:36 AM
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quasi wrote:
>luttgma@gmail.com 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.


Also, since n - a and n + a have the same parity (both even
or both odd), you only need to consider pairs of integers u,v
with u*v = N for which u,v are both even or both odd.

quasi



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