Date: Sun, 25 Jan 1998 16:35:53 -0500
From: josh <xxb1@psu.edu>
To: rusin@math.niu.edu, prem@ix.netcom.com
Subject: Diophantine Equations

Dear Dr. Rusin, Dr. Prem,

    I would like to know if there is a closed form for x, where x is the
largest integer which
cannot be represented by
a_1*p_1+a_2*p_2...+a_n*p_n, where p_n is a set of given positive
integers
with (p_1,p_2,..,p_n)=1, and if we require the coefficients a_i to be
nonnegative
integers.  Obviously for i=2, x=(p_1-1)(p_2-1)-1.  Is there a rapid way
of computing
x, if a closed form does not exist?  Thank you for your help.  I really
enjoyed reading your
web page of diophantines.

                        Sincerely,

                                                Josh Bao
                                                xxb1@psu.edu
==============================================================================

Date: Sun, 1 Feb 1998 00:21:27 -0600 (CST)
From: Dave Rusin <rusin>
To: xxb1@psu.edu
Subject: Re:  Diophantine Equations

I'm almost certain there is no closed form for the number you seek. This is
usually called the "postage stamp problem". It may be discussed in
Guy's "Unsolved Problems in Number Theory"; sorry, I don't have my copy 
handy. There have been a number of papers on this, esp. by Ernst Selmer;
I have here a note that a summary was published 1980 by Ron Graham and
Neal Sloane in one of the SIAM journals. But quite frankly, there is
unlikely to be any pretty result when more than two denominations are
involved.

dave