A Diophantine equation is an equation in which only integers are allowed as coefficients. Also the solutions must be integers. This can be written as ax + by = c. This is a linear diophantine equation.
For non-linar diophantine equations there is no general solution formula available.
Ex. 8x + 7y = 148.
has the solutions x=1 and y = 20.
It can be showed that in order to give integer-solutions 148 must be divisible by the Greatest Common divisor of 8 and 7 in this case 1.