J. V. Leyendekkers and A. G. Shannon

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

Volume 12, 2006, Number 3, Pages 1—9

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## Details

### Authors and affiliations

J. V. Leyendekkers

*The University of Sydney, 2006 Australia*

A. G. Shannon

*Warrane College, Kensington, NSW 1465,
& KvB Institute of Technology, North Sydney, NSW 2060, Australia *

### Abstract

An integer structure (IS) of the sum (*x*^{4} + *y*^{4}) is done using the modular ring Z_{6}. This sum generated many primes and the row structure of such primes is explored. The class functions of the composite factors of this sum are also given, and these, together with the associated row functions, illustrate why it is impossible to produce an integer to the fourth power from such sums. The overall results are consistent with those previously found with IS analysis.

### AMS Classification

- 11A41
- 11A07

### References

- Irving Adler, Nonegenarian Fibonacci Devotee, The Mathematical Intelligencer, 28 (1) (2006): 4.
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_{8}, Notes on Number Theory & Discrete Mathematics. 5 (3) (1999): 102-114. - J.V. Leyendekkers & A.G. Shannon, The Analysis of Twin Primes within Z
_{6}, Notes on Number Theory & Discrete Mathematics. 7 (4) (2001): 115-124 - J.V. Leyendekkers & A.G. Shannon, Powers as a Difference of Squares, Notes on Number Theory & Discrete Mathematics. 8 (3) (2002): 95-106.
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^{nd}edition. Progress in Mathematics, Volume 126. Boston: Birkhäuser, 1994.

## Related papers

## Cite this paper

APALeyendekkers, J. V., and Shannon, A. G. (2006). Integer structure analysis of primes and composites from sums of two fourth powers. Notes on Number Theory and Discrete Mathematics, 12(3), 1-9.

ChicagoLeyendekkers, JV, and AG Shannon. “Integer Structure Analysis of Primes and Composites from Sums of Two Fourth Powers.” Notes on Number Theory and Discrete Mathematics 12, no. 3 (2006): 1-9.

MLALeyendekkers, JV, and AG Shannon. “Integer Structure Analysis of Primes and Composites from Sums of Two Fourth Powers.” Notes on Number Theory and Discrete Mathematics 12.3 (2006): 1-9. Print.