Representations of integers as sums of primes from a Beatty sequence

William D. Banks; Ahmet M. Güloğlu; C. Wesley Nevans

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Representation of a non zero integer as a signed product of primes is unique similarly to its representations in various types of positional notations [4], [3]. The study focuses on counting the prime factors of integers in the form of sums or differences of two equal powers (thus being represented by 1 and a series of zeroes in respective digital bases). Although the introduced theorems are not particularly important, they provide a couple of shortcuts useful for integer factorization,...