# [seqfan] Re: Fixing A175155 Numbers n satisfying n^2 + 1 = x^2 y^3

Robert G. Wilson v rgwv at rgwv.com
Sun Nov 18 16:40:30 CET 2012

```Dear Georgi,

I for one really appreciate your efforts into this sequence.

Sincerely yours, Bob.

-----Original Message-----
From: SeqFan [mailto:seqfan-bounces at list.seqfan.eu] On Behalf Of Georgi
Guninski
Sent: Sunday, November 18, 2012 8:03 AM
To: Sequence Fanatics Discussion list
Subject: [seqfan] Re: Fixing A175155 Numbers n satisfying n^2 + 1 = x^2 y^3

Modulo bugs I checked Pell equations up to 10^6 in less than
1 hour (maybe much faster) and the largest found solutions was for y=3145.

Haven't verified the b-file yet.

Worked with continued fractions and aborted when n was larger than the
limit, which saved time for hard pell eqs.

If someone needs the C++ source let me know.

On Sat, Nov 17, 2012 at 10:50:55PM +0100, Robert Gerbicz wrote:
> Another missing term:
> y=3145;n=3955640265913618377915483821945263099722696409\
> 2919472362788156899442721839388657957656291679526667728\
> 7332760370641317892836601834076118432130864860296617355\
> 5738357207759359869281378421466469507640784572183682794\
> 7089582636783764095008774136131443394961351246331146246\
> 0066620451599501356320569206677478872951346497309792214\
> 8231504626853767310402979432;
>
> and there is no more solution for y<10^5 and n<10^1000.
> (Counted also 292 solutions up to 10^1000, in David's post and in
> b-file there are two more solutions with 1001 digits, so at least 294
> solutions for n<10^1001)
>
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