A recursive definition of -ary addition without carry
Let be a prime number. In this paper we prove that the addition in -ary without carry admits a recursive definition like in the already known cases and .
Let be a prime number. In this paper we prove that the addition in -ary without carry admits a recursive definition like in the already known cases and .
S. S. Pillai proved that for a fixed positive integer , the exponential Diophantine equation , , has only finitely many solutions in integers and . We prove that when is of the form , the above equation has no solution in integers and with .