On integer solutions to x² - dy² = 1, z² - 2dy² =1

• Autorzy: P. G. Walsh
• Języki publikacji: EN

Kategorie tematyczne

• 11D09: Quadratic and bilinear equations

• Wydawca: Institute of Mathematics Polish Academy of Sciences
• Czasopismo: Acta Arithmetica
• Rocznik: 1997
• Tom: 82
• Numer: 1
• Strony: 69-76

Daty

wydano

1997

otrzymano

1996-10-18

poprawiono

1997-02-25

Twórcy

autor

P. G. Walsh

• Department of Mathematics, University of Ottawa, 585 King Edward St., Ottawa, Ontario, Canada K1N 6N5

Bibliografia

• [1] M. A. Bennett, On the number of solutions to simultaneous Pell equations, J. Reine Angew. Math., to appear.
• [2] J. H. E. Cohn, Eight Diophantine equations, Proc. London Math. Soc. (3) 16 (1966), 153-166.
• [3] J. H. E. Cohn, Five Diophantine equations, Math. Scand. 21 (1967), 61-70.
• [4] J. H. E. Cohn, The Diophantine equation x⁴-Dy²=1, II, Acta Arith. 78 (1997), 401-403.
• [5] W. Ljunggren, Zur Theorie der Gleichung x²+1=Dy⁴, Avh. Norske Vid. Akad. Oslo (1942), 1-27.
• [6] D. W. Masser, Open Problems, in: Proc. Sympos. Analytic Number Theory, W. W. L. Chen (ed.), London Imperial College, 1985.
• [7] K. Ono, Euler's concordant forms, Acta Arith. 78 (1996), 101-123.
• [8] N. Robbins, On Pell numbers of the form px², where p is a prime, Fibonacci Quart. (4) 22 (1984), 340-348.
• [9] P. Samuel, Algebraic Theory of Numbers, Houghton Mifflin, Boston, 1970.
• [10] W. Sierpiński, Elementary Theory of Numbers, Państwowe Wydawnictwo Naukowe, Warszawa, 1964.
• [11] C. L. Stewart, On divisors of Fermat, Fibonacci, Lucas and Lehmer numbers III, J. London Math. Soc. (2) 28 (1983), 211-217.