## Coin Problem

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.