Characterization and Extendability of P k Sets For k=3(4)

Year 2010, Volume: 23 Issue: 3, 295 - 297, 06.07.2010

Hüseyin Altındiş

Abstract

ABSTRACT

In this paper the characterization of certain families of the Pk   sets for k=3(4) are given, and it is shown that some of them can not be extended.

 

Key Words: Diophantine Equation, Congruence, Legendre Symbol

Keywords

Diophantine Equation, Congruence, Legendre Symbol

Characterization and Extendability of P Sets For k ≡ k

Abstract

References

• Dickson, L. E., “History of the theory of numbers”, Chelsea New York, 2: Sayfa no (1966).
• Baker A. and Davenport H., “The equations x2− = y2 and 8x− Math. Oxford Ser., 2(3):129-137 (1969) = − z2”, Quart. J.
• Kanagasababathy P. and Ponnuduraı, T. “The Simultaneous y233 −3 Math.Oxford Ser, 26(3): 275-278 (1975). x2= −”, Quart. J. − ”, Quart. J.
• Heichelheim, P, “The study of positive integers (a b such that ab + is a square. Fibonacci ,) such that ab + is a square. Fibonacci Quatr., 17: 269-274 (1979).
• Thamotherampillai, N., “The set of numbers {1 2 7}”,Bulletin Calcutta Math. Soc. 72:195- (1980).
• Mohanty S.P. and Ramasamy, A.M.S. “The simultaneous Diophantine equations 5y− x =x and 2y+ = + = z2” J.Number Theory, 18: 356-359 (1984).
• Mohanty S.P. and Ramasamy A.M.S., The Characteristic number of two simultaneous Pell’s equations and it’s application. Simon Stevin”, A Quarterly J.P. and Applied Math., 59: 203-214 (1985)
• Brown, E. “Sets in which xy+ k is always a square. Mathematics of Comp.”, 613-620 (1985). Altindis, H., “On P j2
• Calcutta”, Mathematical Society, 86(4): 305 - 306. (1994).
• Dujella, A., “On the size of Diophantine m tuples”, Math. Proc. Cambridge Philos Soc., :23-33 (2002).
• Dujella A.and Luca, F., “Diophantine m tuples for primes”. Intern. Math. Research Notices :2913-2940 (2005).
• Dujella A. and. Ramasamy, A. M. S, “Fibonacci numbers and sets with the property D (4)”, Bull. Belg. Math. Soc., Simon Stevin, 12:401-412 (2005).