Thread: Sock Drawer
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Old 09-16-2003, 04:25 PM
thylacine thylacine is offline
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Join Date: Jul 2003
Posts: 294
Default all(?) solutions

It just struck me that solving 2R^2=T^2+1 is related to the continued fraction for sqrt(2).

The bottom line is that if (R,T) is a solution, then so is (3R+2T,4R+3T).

Starting with (R,T)=(1,1) you generate infinitely many solutions, and I think these might be all.

So Solutions are (R,T)=(1,1), (5,7), (29,41), (169,239), ...

Then translate back to get solutions (r,t) to t(t-1) = 2r(r-1).

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