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Topic: Squares on a line ...
Replies: 16   Last Post: May 9, 2011 7:30 PM

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 Iain Davidson Posts: 1,173 Registered: 12/12/04
Re: Squares on a line ...
Posted: May 7, 2011 8:41 AM

On May 6, 5:29 pm, "alainvergh...@gmail.com" <alainvergh...@gmail.com>
wrote:
> Bonsoir,
>
> I've got the line  l(x) = 84x - 227 ,
> points 3,9,19,29,47,77.
> and l(3),l(9), ...l(77)  are exact squares.
>
> Do you know a way to define such points?

You seem to be looking for integer
solutions to

y^2 = 84x - 227

y^2 = 84x - 3*84 +25

y^2 -25 = 84x- 3*84

(y+5)(y-5) = 84x - 3*84

(y+5)(y-5)/84 = x - 3

(y+5)(y-5) = 84k

If y+5 = {.., -1,0,1, ..}
y-5 = {..,-84,0,84,..}

then y = {.., -6,-5,-4, ..}
y = {..,-79,5,89,..}

Solutions are y = {..,-79,5,89,..}

If y+5 = {.., -2,0,2, ..}
y-5 = {..,-42,0,42,..}

then y = {.., -7,-5,-3, ..}
y = {..,-37,-5,37,..}

Solutions are y = {..,-37,-5,37,..}

and so on