On the number of solutions of the Diophantine equation of Frobenius - General case

By Takao Komatsu. 2003

46 citations recorded by the source corpus.

We determine the number of solutions of the equation a1x1 + a2x2 + ··· + amxm = b in non-negative integers x1, x2, ... , xn .I f m =2 , then the largest b for which no solution exists is a1a2 − a1 − a2, and an explicit formula for the number of solutions is known. In this paper we give the method for computing the desired number. The method is illustrated with several examples.

View Paper: https://www.semanticscholar.org/paper/8dbbcc40c61f55071c0ecf71f80caf317f7641ad