[seqfan] Re: Minimal k > n such that (4k+3n)(4n+3k) is square

Charles Greathouse charles.greathouse at case.edu
Sun Dec 22 04:56:47 CET 2013


I had tested my conjecture to 10^4, but no luck on a proof yet.

Charles Greathouse
Analyst/Programmer
Case Western Reserve University


On Fri, Dec 20, 2013 at 9:57 PM, Hans Havermann <gladhobo at teksavvy.com>wrote:

> For small n, empirically, whenever there exists a solution between 109n/4
> and 393n, there is a corresponding solution (but, what is the
> correspondence?) between n and 109n/4.
>
> 13  {916}  {132}
> 24  {2509}  {157}
> 26  {1832}  {264}
> 33  {1657}  {481}
> 37  {4888}  {184}
> 39  {2748}  {396}
> 48  {5018}  {314}
> 52  {3664,8053}  {528,213}
> 61  {2616}  {1048}
> 65  {4580}  {660}
> 66  {3314}  {962}
> 69  {12004}  {244}
> 72  {7527}  {471}
> 73  {6457}  {577}
> 74  {9776}  {368}
> 78  {5496}  {792}
> 88  {5037,16741}  {1117,277}
> 91  {6412}  {924}
> 96  {10036}  {628}
> 97  {3793}  {1833}
> 99  {4971}  {1443}
> 104  {7328,16106}  {1056,426}
> 109  {22264}  {312}
>
> On Dec 20, 2013, at 4:29 PM, Charles Greathouse <
> charles.greathouse at case.edu> wrote:
>
> > If there is no n < k < 109n/4 with (4k+3n)(4n+3k) square, then a(n) =
> 393n.
>
>
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