Marius Coman
Abstract
In this paper I make the following two conjectures: (I) For any prime p, p > 5, there exist n positive integer such that the sum of the digits of the number p*2^n is divisible by p; (II) For any prime p, p > 5, there exist an infinity of positive integers m such that the sum of the digits of the number p*2^m is prime.
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In this paper I make the following two conjectures: (I) For any prime p, p > 5, there exist n positive integer such that the sum of the digits of the number p*2^n is divisible by p; (II) For any prime p, p > 5, there exist an infinity of positive integers m such that the sum of the digits of the number p*2^m is prime.
Key concepts: Mathematics, Infinity, Integer (computer science), Combinatorics, Number theory, Prime (order theory), Prime factor, Prime number