Numerical Semigroups with two coprime generators: James J. Sylvester's proof

This paper examines in a new way some known facts about numerical semigroups especially when the number of minimal generators (that is the embedding dimension) is at most three and at least two minimal generators are coprime; for such semigroups an algorithm is re-investigated to find the pseudo-Frobenius numbers. We consider particular $\langle a,a+1,a+p\rangle$ for some $p\ge 2$, $\langle ab+a+1,bc+b+1,ca+c+1\rangle$ and $\langle n^2,(n+1)^2,(n+2)^2\rangle$ semigroups; a certain family of $n$ dimensional numerical semigroups of type at most $n-1$ is also given.Comment: Corrections in the last sectio