Definition:Diophantine Equation/Linear Diophantine Equation
A linear Diophantine equation is a Diophantine equation in which all the arguments appear to no higher than the first degree.
- $ax + by + c = 0$
- $a_1 x_1 + a_2 x_2 + \cdots + a_n x_n = b$
- $15 x + 27 y = 1$
has no solutions for $x$ and $y$ integers.
- $5 x + 6 y = 1$
has the general solution:
- $x = -1 + 6 t, y = 1 - 5 t$
- Results about linear diophantine equations can be found here.
Source of Name
This entry was named for Diophantus of Alexandria.