| Peter:
Why is it called the Frobenius Problem?
Are there restrictions on a1, a2, ..., ak? If k = 2, a1 = 5, and
a2 = 10, are the values that cannot be achieved = {1,2,3,4,6,7,8,9,11,
12,...}, or something else?
John
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| This problem is named after the German mathmematician Frobenius, apparently
because of a comment by Brauer that "Frobenius mentioned it occasionally in
his lectures".
For the problem to make sense, assume that gcd(a1,a2,...,ak) = 1, and that
all a1,a2,...,ak are > 1. Also, assume that a1,a2,...,ak are independent:
that none can be represented as a linear combination with nonnegative integer
coefficients of the others.
For example g(5,7) = 23, and g(5,7,9) = 13.
[ The problem is shown to be related to Shellsort in this month's issue of
the Journal of Algorithms. A bibliography can also be found there. ]
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