J. V. Leyendekkers and A. G. Shannon

Notes on Number Theory and Discrete Mathematics, ISSN 1310-5132

Volume 16, 2010, Number 1, Pages 1—4

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## Details

### 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, Australia*

### Abstract

Using the modular ring Z_{4}, it is shown that the row structures of *x ^{n}* −

*y*,

^{n}*x*,

*y*odd,

*n*= 2

*, are incompatible with the row structures of*

^{m}*z*. Even though some structures are close, the right-end-digits (REDs) are quite distinct. The analysis shows how the effort to find counter-examples for such theorems may be drastically reduced.

^{n}### Keywords

- Primes
- Composites
- Modular rings
- Right-end digits
- Integer structure

### AMS Classification

- 11A41
- 11A07

### References

- Leyendekkers, J.V., A.G. Shannon. 2006. Integer Structure Analysis of Primes and Composites from Sums of Two Fourth Powers. Notes on Number Theory & Discrete Mathematics. 12(3): 1-9.
- Leyendekkers, J.V., A.G. Shannon. 2007. Modular Ring Class Structures of x
^{n}± y^{n}. Notes on Number Theory & Discrete Mathematics. 13(3): 27-35. - Leyendekkers, J.V., A.G. Shannon. 2009. The Integer Structure of the Difference of Two Odd-Powered Odd Integers. Notes on Number Theory & Discrete Mathematics. 15(3): 14-20.

## Related papers

## Cite this paper

APALeyendekkers, J. V., and Shannon, A. G. (2010). The integer structure of the difference of two odd integers raised to an even power. Notes on Number Theory and Discrete Mathematics, 16(1), 1-4.

ChicagoLeyendekkers, JV, and AG Shannon. “The Integer Structure of the Difference of Two Odd Integers Raised to an Even Power.” Notes on Number Theory and Discrete Mathematics 16, no. 1 (2010): 1-4.

MLALeyendekkers, JV, and AG Shannon. “The Integer Structure of the Difference of Two Odd Integers Raised to an Even Power.” Notes on Number Theory and Discrete Mathematics 16.1 (2010): 1-4. Print.