Parity of number of partitions of an integer

Richard Guy rkg at
Thu Sep 4 01:02:38 CEST 2003

I haven't looked at these papers:

89j:11100 Hirschhorn, M. D.; Subbarao, M. V.
On the parity of $p(n)$.  
Acta Arith.  50  (1988),  no. 4, 355--356. 

93j:11068 Hirschhorn, M. D.
On the parity of $p(n)$. II.  J. Combin. 
Theory Ser. A  62  (1993),  no. 1, 128--138.

Evidently one should also look at MR 8, 566g, Gupta;
MR 11, 13d, Majumdar; MR 22#6778, Morris Newman;
MR 22#7995, Kolberg -- p(n) is both odd and even
infinitely often; MR 25#3892, Newman;
MR 50#9823, Subbarao; MR 82d::10025, Hirschhorn;
MR 87k:11113, Blecksmith, Brillhart,Gerst;


On Wed, 3 Sep 2003, John Conway wrote:

> On Wed, 3 Sep 2003, Brendan McKay wrote:
> > Is there a formula for the parity of the number of partitions
> > of an integer?  It is A040051.
>    This is an old question, to which nobody seems to have found even
> a partial answer - a bit surprising in view of the fact that there 
> are simple infinite sequences of numbers for which we know the
> value of  p(n)  modulo 5 or 7 or 11.
>       John Conway

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