# On arithmetic progressions with equal products

N. Saradha; T. N. Shorey; R. Tijdeman

Acta Arithmetica (1994)

- Volume: 68, Issue: 1, page 89-100
- ISSN: 0065-1036

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topN. Saradha, T. N. Shorey, and R. Tijdeman. "On arithmetic progressions with equal products." Acta Arithmetica 68.1 (1994): 89-100. <http://eudml.org/doc/206646>.

@article{N1994,

author = {N. Saradha, T. N. Shorey, R. Tijdeman},

journal = {Acta Arithmetica},

keywords = {exponential diophantine equation; effective method},

language = {eng},

number = {1},

pages = {89-100},

title = {On arithmetic progressions with equal products},

url = {http://eudml.org/doc/206646},

volume = {68},

year = {1994},

}

TY - JOUR

AU - N. Saradha

AU - T. N. Shorey

AU - R. Tijdeman

TI - On arithmetic progressions with equal products

JO - Acta Arithmetica

PY - 1994

VL - 68

IS - 1

SP - 89

EP - 100

LA - eng

KW - exponential diophantine equation; effective method

UR - http://eudml.org/doc/206646

ER -

## References

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- [2] B. Brindza, On S-integral solutions of the equation ${y}^{m}=f\left(x\right)$, 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. Zbl0206.05602
- [6] L. J. Mordell, On the integer solutions of y(y+1) = x(x+1)(x+2), Pacific J. Math. 13 (1963), 1347-1351. Zbl0124.27402
- [7] T. J. Rivlin, The Chebyshev Polynomials, Wiley, New York, 1974. Zbl0299.41015
- [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. Zbl0716.11017
- [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. Zbl0757.11010
- [10] N. Saradha and T. N. Shorey, On the equation (x+1)...(x+k) = (y+1)...(y+mk), Indag. Math. 3 (1992), 79-90. Zbl0757.11011
- [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. Zbl0763.11013
- [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). Zbl0763.11013
- [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. Zbl0833.11010
- [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. Zbl0606.10011

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