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In this note we recall the definition of the digital root, and apply thenotion of the digital root to searching solutions of Diophantine equations. Atable of arithmetic operations with digital roots is given. This method isincapable of obtaining complete solutions of equations, but it is frequentlyuseful in determining whether this equation is solvable in integers or not. Aminor extension of Fermat's little theorem is put forward.

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