Authors and affiliations
J. V. Leyendekkers
The University of Sydney, 2006 Australia
A. G. Shannon
Warrane College, The University of New South Wales
Kensington, NSW 1465
& RafflesKvB Institute Pty Ltd
North Sydney, NSW, 2060, Australia
Integer structure theory is used to analyse the factors of sums and differences of two identical powers of two integers, x and y. For instance, the sum of two identical powers, m, cannot form primes when m is odd or when m is even if the powers are odd and of the form m/2. The expanded forms of the factors indicate why the structure acts against the sum ever equalling an identical power. The difference of odd powers can yield primes when x − y = 1. The difference of even powers cannot yield primes whereas the sum can when m/2n is even. However, x2 − y2 can equal a prime when x − y = 1.
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Cite this paper
Leyendekkers, J. V., and Shannon, A. G. (2007). Modular-ring class structures of xn ± yn. Notes on Number Theory and Discrete Mathematics, 13(3), 27-35.