# Diophantus

**Diophantus** has been called the "Father of
Algebra." He lived during the period from 250 to 350 A.D.,
"a silver age in mathematics." His text *the
Arithmetica* was composed of 13 books and 189 problems.

The problems he worked on were mostly linear systems of equations with a few quadratics. He included strong hints to make the questions easier to solve. One of these problems uses his age as a solution, so he apparently lived to at least 84.

Diophantus introduced symbols for subtraction, for an
unknown, and for the degree of the variable. Although there
were several solutions to some of his problems, he only
looked for one positive integer solution. Now we call an
equation to be solved in integers a **diophantine
equation**. For example, Diophantus considered the
equations

ax+by=c

where the variables *x* and *y* are positive
integers. This equation is solvable if and only if the
greatest common divisor
of *a* and *b* divides *c*. We can
find the solution to these equations using a modified
Euclidean Algorithm.

This entry edited from a contribution by Jimmy Goodman.