On the equation x(x+1)... (x+k-1) = y(y+d)... (y+(mk-1)d), m=1,2

• Autorzy: N. Saradha , T.N. Shorey , R. Tijdeman
• Języki publikacji: EN
• Wydawca: Institute of Mathematics Polish Academy of Sciences
• Czasopismo: Acta Arithmetica
• Rocznik: 1995
• Tom: 71
• Numer: 2
• Strony: 181-196

Daty

wydano

1995

otrzymano

1994-10-26

Twórcy

autor

N. Saradha

• School of Mathematics, Tata Institute of Fundamental Research, Homi Bhabha Road, Bombay 400 005, India

autor

T.N. Shorey

• School of Mathematics, Tata Institute of Fundamental Research, Homi Bhabha Road, Bombay 400 005, India

autor

R. Tijdeman

• Mathematical Institute, Leiden University, P.O. Box 9512, 2300 RA Leiden, The Netherlands

Bibliografia

• [1] A. Baker, Bounds for the solutions of the hyperelliptic equation, Proc. Cambridge Philos. Soc. 65 (1969), 439-444.
• [2] L. E. Dickson, History of the Theory of Numbers, Vol. II, first publ. in 1919. Reprint: Chelsea, New York, 1971.
• [3] Ya. Gabovich, On arithmetic progressions with equal products of terms, Colloq. Math. 15 (1966), 45-48 (in Russian).
• [4] Problèmes P543 et P545, R1, Colloq. Math. 19 (1968), 179-180.
• [5] N. Saradha and T. N. Shorey, On the ratio of two blocks of consecutive integers, Proc. Indian Acad. Sci. Math. Sci. 100 (1990), 107-132.
• [6] N. Saradha and T. N. Shorey, On the equation x(x+d₁) ... (x + (k-1)d₁) = y(y+d₂) ... (y + (mk-1)d₂), Proc. Indian Acad. Sci. Math. Sci. 104 (1994), 1-12.
• [7] N. Saradha, T. N. Shorey and R. Tijdeman, On arithmetic progressions of equal lengths with equal products, Math. Proc. Cambridge Philos. Soc., to appear.
• [8] T. N. Shorey and R. Tijdeman, Perfect powers in products of terms in an arithmetical progression (II), Compositio Math. 82 (1992), 119-136.