Sets in which xy + k is always a square

Mathematics of Computation

Volumn 45, Issue 172, 1985, Pages 613-620

  Brown, Ezra ^a  

^a VIRGINIA POLYTECHNIC INSTITUTE AND STATE UNIVERSITY   (United States)

Author keywords

[No Author keywords available]

Indexed keywords

EID: 84966212584     PISSN: 00255718     EISSN: None     Source Type: Journal    
DOI: 10.1090/S0025-5718-1985-0804949-7     Document Type: Article

References (9)

1. A. Baker H. Davenport, "The equations 3x2 - 2 = y2 and 8x2 - 7 = z2, " Quart. J. Math. Oxford Ser. (3), v. 20, 1969, p. 129-137.
2. L. E. Dickson, History of the Theory of Numbers, vol. 2, Carnegie Institute, Washington, 1920; reprinted, Chelsea, New York, 1966.
3. C. M. Grinstead, "On a method of solving a class of Diophantine equations, " Math. Comp., v. 32, 1978, p. 936-940.
4. P. Heichelheim, "The study of positive integers (a, b) such that ah + 1 is a square." Fibonacci Quart., v. 17, 1979, p. 269-274.
5. P. K. ANAGASABAPATHY T. PONNUDURAI, "The simultaneous Diophantine equations v2 - 3.x2 =- 2 and z2 - 8x2 = - 7, " Quart. J. Math. Oxford Ser. (3), v. 26, 1975, p. 275-278.
6. S. P. Mohanty A. M. S. Ramasamy, "The simultaneous Diophantine equations 5Y2 - 20 = X2 and 2V2 + 1 = Z2, " J. Number Theory, v. 18, 1984, p. 356-359.
7. T. Nagell, Introduction to Number Theory, Wiley, New York, 1951.
8. G. Sansone, "II sistema diofanteo N + 1 = x2, 3A/+ 1 = y2, 8/V + 1 = z2, " Ann. Mat. Pura Appl. (4), v. 3, 1976, p. 125-151.
9. N. Thamotherampillai, "The set of numbers (1, 2, 7), " Bull. Calcutta Math. Soc, v. 72, 1980, p. 195-197.