Coin Problem
Let there be 
Integers 
with 
(all Relatively Prime). For large enough 
, there is a solution in NonnegativeIntegers 
. The greatest 
for which there is no solution is called thecoin 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.
- Euler's Conjecture
- Euler's Criterion
- Euler's Displacement Theorem
- Euler's Distribution Theorem
- Euler's Factorization Method
- Euler's Finite Difference Transformation
- Euler's Graeco-Roman Squares Conjecture
- Euler's Homogeneous Function Theorem
- Euler's Hypergeometric Transformations
- Euler's Idoneal Number
- Euler's Machin-Like Formula
- Euler's Pentagonal Number Theorem
- Euler's Phi Function
- Euler's Polygon Division Problem
- Euler's Quadratic Residue Theorem
- Euler Square
- Euler's Rotation Theorem
- Euler's Rule
- Euler's Series Transformation
- Euler's Spiral
- Euler's Sum of Powers Conjecture
- Euler's Theorem
- Euler's Totient Rule
- Euler's Transform
- Euler's Triangle