Optic equation

In number theory, the optic equation is an equation that requires the sum of the reciprocals of two positive integers a and b to equal the reciprocal of a third positive integer c:^[1]

${\displaystyle {\frac {1}{a}}+{\frac {1}{b}}={\frac {1}{c}}.}$

Multiplying both sides by abc shows that the optic equation is equivalent to a Diophantine equation (a polynomial equation in multiple integer variables).