Studying solutions to Diophantine equations using the table of $N$th digital roots of integers

In this note we recall the definition of the digital root, and apply the notion of the digital root to searching solutions of Diophantine equations. A table of arithmetic operations with digital roots is given. This method is incapable of obtaining complete solutions of equations, but it is frequently useful in determining whether this equation is solvable in integers or not. A minor extension of Fermat's little theorem is put forward.