## Diophantine Equations

Named after *Diophantus of Alexandria* ( ca. 250 A.D. ), who in his book *Arithmetica*
seeks to solve linear and square equations and especially to find their integer solutions.

The program computes the integral solutions of the equation a·x - b = m·y with m > 0 .

This for example permits the determination of the integral points in a straight line.

### Example:

The straight line with the equation y = 7/3·x - 5/3 ⇔ 7·x - 3·y - 5 = 0 ; x,y integer

comprises the integer points

L = { (x/y) | x=2+3t, y=3+7t and t integer }
= { (2/3),(5/10),(-1/-1),(8/17), ... }

### See also:

Wikipedia: Diophantine Equations