not the diff. of two prime powers

ZAKIRS zfseidov at
Sun Oct 13 10:18:56 CEST 2002

Neil, and all!
after so much long discussion of people expert in the field, 
let me express my humble opinion
there's need for some classification: 
even in the subject Neil writes about prime powers which is not (?!) the

One may talk on the different possible cases for pp m^p:  
a)only prime base m
b)only prime degree p
c)both prime base and degree m and p
d)the special case of squares/cubes (again with prime or composite base )
The problem of d=m^p-n^p (i call it for myseld dmpnq - like "demping"
may be different in these cases.zak

p.s. really "prime power" quite may be prime power of composite base, 
or composite power of prime base, or anything else

-----Original Message-----
From: N. J. A. Sloane [mailto:njas at]
Sent: Sunday, October 13, 2002 3:43 AM
To: seqfan at; njas at; djr at;
judmccr at; zfseidov at; seidovzf at;
Subject: Re: not the diff. of two prime powers.

I've added Don's version as A066510.  The two main sequences are now
(I only give the first 5 lines, see the database for the full, lengthy,

%I A074981
%S A074321
%T A074321 182,202,206,210,226,230,238,246,254,258,266,274,278,302,306,310,
%U A074321 314,322,326,330,358,374,378,390,394,398,402,410,418,422,426,430
%N A074981 Conjectured list of positive numbers which are not of the form
m^p-n^q, where m,n,p,q are integers with m>0, n>0, p>1, q>1.

%I A066510
%S A066510 6,14,34,42,58,62,66,70,78,86,90,102,110,114,130,158,178,182,202,
%T A066510 210,230,238,254,258,266,274,278,302,306,310,314,322,326,330,358,
%U A066510 374,378,390,394,398,402,410,418,422,426,430,434,438,446,450,454
%N A066510 Conjectured list of positive numbers which are not of the form
m^p-n^q, where m,n,p,q are integers with p>1, q>1.

and if you forget the sequence numbers, do what i do and refer
to the index, where there is this line:

powers, not the difference of two: A074981*, A074980, A069586, A023057,


PS but wait a couple of hours before checking the database,
i'm in the middle of an update

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