Let there be Integers
with
(all
Relatively Prime). For large enough
, there is a solution in Nonnegative
Integers . The greatest
for which there is no solution is called the
coin problem. Sylvester showed

and an explicit solution is known for , but no closed form solution is known for larger .

**References**

Guy, R. K. ``The Money-Changing Problem.'' §C7 in
*Unsolved Problems in Number Theory, 2nd ed.* New York: Springer-Verlag,
pp. 113-114, 1994.

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1999-05-26