Algebra

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
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