Are there any softwares which can solve equations from number theory?

Question

Are there any softwares which can solve equations from number theory? For example, solve equations $x+y+z=100$, $x\equiv 2~{(\rm mod~5)}$, $y\equiv 3~{(\rm mod~7)}$, $2x+3y=50$, where $x,y,z$ are positive integers. Is there a software that can do this work?