Integral Sequences of Infinite Length Whose Terms Are Relatively Prime

ABSTRACT

It is given in Weil and Rosenlicht ([1], p. 15) that (resp. 2) for all non-negative integers *m* and *n *with* m≠n* if *c* is any even (resp. odd) integer. In the present paper we generalize this. Our purpose is to give other integral sequences such that G.C.D.(*y _{m}*,

KEYWORDS

Relatively Prime; Integral Sequences of Infinite Length; Sets of Infinitely Many Prime Numbers

Relatively Prime; Integral Sequences of Infinite Length; Sets of Infinitely Many Prime Numbers

Cite this paper

K. Hatada, "Integral Sequences of Infinite Length Whose Terms Are Relatively Prime,"*Advances in Pure Mathematics*, Vol. 3 No. 1, 2013, pp. 24-28. doi: 10.4236/apm.2013.31005.

K. Hatada, "Integral Sequences of Infinite Length Whose Terms Are Relatively Prime,"

References

[1] A. Weil and M. Rosenlicht, “Number Theory for Beginners,” Springer Verlag, New York, 1979. doi:10.1007/978-1-4612-9957-8

[2] G. H. Hardy and E. M. Wright, “An Introduction to the Theory of Numbers,” 4th Edition, Oxford University Press, Ely House, London, 1971.

[3] A. Baker, “A Concise Introduction to the Theory of Numbers,” Cambridge University Press, Cambridge, 1984. doi:10.1017/CBO9781139171601

[4] B. J. Birch, “Cyclotomic Fields and Kummer Extensions,” In: J. W. S. Cassels and A. Fr?hlich, Eds., Algebraic Number Theory, Academic Press, London, 1967, pp. 85-93.

[5] S. Lang, “Algebraic Number Theory,” Addison-Wesley Publishing Company, Massachusetts, 1970.

[6] S. Lang, “Algebra,” 3rd Edition, Springer Verlag, New York, 2002. doi:10.1007/978-1-4613-0041-0

[7] E. Weiss, “Algebraic Number Theory,” 2nd Edition, Chelsea Publishing Company, New York, 1976.

[8] H. Weyl, “Algebraic Theory of Numbers,” Princeton University Press, Princeton, 1940.

[9] J.-P. Serre, “Local Fields,” Springer Verlag, New York, 1979.

[1] A. Weil and M. Rosenlicht, “Number Theory for Beginners,” Springer Verlag, New York, 1979. doi:10.1007/978-1-4612-9957-8

[2] G. H. Hardy and E. M. Wright, “An Introduction to the Theory of Numbers,” 4th Edition, Oxford University Press, Ely House, London, 1971.

[3] A. Baker, “A Concise Introduction to the Theory of Numbers,” Cambridge University Press, Cambridge, 1984. doi:10.1017/CBO9781139171601

[4] B. J. Birch, “Cyclotomic Fields and Kummer Extensions,” In: J. W. S. Cassels and A. Fr?hlich, Eds., Algebraic Number Theory, Academic Press, London, 1967, pp. 85-93.

[5] S. Lang, “Algebraic Number Theory,” Addison-Wesley Publishing Company, Massachusetts, 1970.

[6] S. Lang, “Algebra,” 3rd Edition, Springer Verlag, New York, 2002. doi:10.1007/978-1-4613-0041-0

[7] E. Weiss, “Algebraic Number Theory,” 2nd Edition, Chelsea Publishing Company, New York, 1976.

[8] H. Weyl, “Algebraic Theory of Numbers,” Princeton University Press, Princeton, 1940.

[9] J.-P. Serre, “Local Fields,” Springer Verlag, New York, 1979.