On arithmetic progressions with equal products

• Autorzy: N. Saradha , T. N. Shorey , R. Tijdeman
• Języki publikacji: EN
• Wydawca: Institute of Mathematics Polish Academy of Sciences
• Czasopismo: Acta Arithmetica
• Rocznik: 1994
• Tom: 68
• Numer: 1
• Strony: 89-100

Daty

wydano

1994

otrzymano

1994-03-23

Twórcy

autor

N. Saradha

• School of Mathematics, Tata Institute of Fundamental Research, Homi Bhabha Road, Bombay 400005, India

autor

T. N. Shorey

• School of Mathematics, Tata Institute of Fundamental Research, Homi Bhabha Road, Bombay 400005, India

autor

R. Tijdeman

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

Bibliografia

• [1] D. W. Boyd and H. H. Kisilevsky, The diophantine equation u(u+1)(u+2)(u+3) = v(v+1)(v+2), Pacific J. Math. 40 (1972), 23-32.
• [2] B. Brindza, On S-integral solutions of the equation $y^m = f(x)$, Acta Math. Hungar. 44 (1984), 133-139.
• [3] J. W. S. Cassels, Factorization of polynomials in several variables, in: Proc. 15th Scandinavian Congress, Oslo 1968, Lecture Notes in Math. 118, Springer, 1970, 1-17.
• [4] A. Ehrenfeucht, A criterion for absolute irreducibility of polynomials, Prace Mat. 2 (1958), 167-169 (in Polish).
• [5] R. A. MacLeod and I. Barrodale, On equal products of consecutive integers, Canad. Math. Bull. 13 (1970), 255-259.
• [6] L. J. Mordell, On the integer solutions of y(y+1) = x(x+1)(x+2), Pacific J. Math. 13 (1963), 1347-1351.
• [7] T. J. Rivlin, The Chebyshev Polynomials, Wiley, New York, 1974.
• [8] 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.
• [9] N. Saradha and T. N. Shorey, On the equation (x+1)...(x+k) = (y+1)...(y+mk) with m = 3,4, Indag. Math. 2 (1991), 489-510.
• [10] N. Saradha and T. N. Shorey, On the equation (x+1)...(x+k) = (y+1)...(y+mk), Indag. Math. 3 (1992), 79-90.
• [11] N. Saradha and T. N. Shorey, On the equation x(x+d)...(x+(k-1)d) = y(y+d)...(y+(mk-1)d), Indag. Math. 3 (1992), 237-242.
• [12] 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).
• [13] N. Saradha, T. N. Shorey and R. Tijdeman, On arithmetic progressions of equal lengths with equal products, Math. Proc. Cambridge Philos. Soc., to appear.
• [14] A. Schinzel, Selected Topics on Polynomials, University of Michigan Press, Ann Arbor, 1982.
• [15] T. N. Shorey and R. Tijdeman, Exponential Diophantine Equations, Cambridge University Press, 1986.