Modular-ring class structures of xn ± yn

J. V. Leyendekkers and A. G. Shannon
Notes on Number Theory and Discrete Mathematics, ISSN 1310-5132
Volume 13, 2007, Number 3, Pages 27—35
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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 xy = 1. The difference of even powers cannot yield primes whereas the sum can when m/2n is even. However, x2y2 can equal a prime when xy = 1.

AMS Classification

  • 11A41
  • 11A07


  1. Craig, Maurice. The Composition Heresies. The Australian Mathematical Society Gazette. Vol.33, No.4(2006), 265-272.
  2. Dickson, L.E. History of the Theory of Numbers. Volume 3. New York: Chelsea, 1952.
  3. Leyendekkers, J.V., A.G. Shannon, Integer Structure Analysis of Primes and Composites from (x4 + y4). Notes on Number Theory & Discrete Mathematics. Submitted.
  4. Rouse Ball, W.W. History of Mathematics. New York: Dover, 1960.

Related papers

  1. Leyendekkers, J. V.,  & Shannon, A. G. (2009). The integer structure of the difference of two odd-powered odd integers. Notes on Number Theory and Discrete Mathematics, 15(3), 14-20.

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.

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