The Math Forum

Search All of the Math Forum:

Views expressed in these public forums are not endorsed by NCTM or The Math Forum.

Math Forum » Discussions » sci.math.* » sci.math.research

Notice: We are no longer accepting new posts, but the forums will continue to be readable.

Topic: Linear Combination of Non-negative integers.
Replies: 4   Last Post: Aug 26, 2000 11:24 AM

Advanced Search

Back to Topic List Back to Topic List Jump to Tree View Jump to Tree View   Messages: [ Previous | Next ]
Robert Hill

Posts: 529
Registered: 12/8/04
Re: Linear Combination of Non-negative integers.
Posted: Aug 22, 2000 4:46 PM
  Click to see the message monospaced in plain text Plain Text   Click to reply to this topic Reply

In article <>, Pierre Bornsztein <> writes:

> according to Guy's "unsolved problems in number theory" Springer p.113
> (C7), this result is due to Sylvester (1884), who also proved that the
> number of non-representable numbers is (a-1)(b-1)/2.
> The general problem with n > 1 numbers is known as the coin exchange
> problem of Frobenius.
> The case n = 3 has been solved by Selmer and Beyer, then simplified by
> Rödseth and later by Greenberg. But there is no formula as simple as
> above.
> For n > 3, only bounds are known.

This is the basis of Conway's game of "Sylver Coinage", named in honour
of Sylvester (see Berlekamp, Conway and Guy, "Winning Ways", vol. 2).

The basic results for n=2 numbers are so easy (for example, I was able
to independently rediscover and prove them, and I'm pretty dim) that I
wonder if somebody knew them before Sylvester (whose contribution was
not limited to the case n=2). Maybe an earlier publication has been
overlooked, or somebody knew the stuff but didn't trouble to publish it.

Robert Hill

Point your RSS reader here for a feed of the latest messages in this topic.

[Privacy Policy] [Terms of Use]

© The Math Forum at NCTM 1994-2018. All Rights Reserved.