Squares in products with terms in an arithmetic progression

• Autorzy: N. Saradha
• Języki publikacji: EN

Kategorie tematyczne

• 11D61: Exponential equations

• Wydawca: Institute of Mathematics Polish Academy of Sciences
• Czasopismo: Acta Arithmetica
• Rocznik: 1998
• Tom: 86
• Numer: 1
• Strony: 27-43

Daty

wydano

1998

otrzymano

1997-07-15

poprawiono

1998-03-16

Twórcy

autor

N. Saradha

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

Bibliografia

• [1] T. M. Apostol, Introduction to Analytic Number Theory, Springer, 1976.
• [2] L. E. Dickson, Introduction to the Theory of Numbers, Univ. of Chicago Press, 1946.
• [3] L. E. Dickson, History of the Theory of Numbers, Vol. II, Washington, 1919; reprint: Chelsea, New York, 1971.
• [4] P. Erdős, Note on products of consecutive integers, J. London Math. Soc. 14 (1939), 194-198.
• [5] P. Erdős and J. L. Selfridge, The product of consecutive integers is never a power, Illinois J. Math. 19 (1975), 292-301.
• [6] W. Ljunggren, New solution of a problem proposed by E. Lucas, Norsk Mat. Tidsskrift 34 (1952), 65-72.
• [7] R. Marsza/lek, On the product of consecutive elements of an arithmetic progression, Monatsh. Math. 100 (1985), 215-222.
• [8] A. Meyl, Question 1194, Nouv. Ann. Math. (2) 17 (1878), 464-467.
• [9] L. J. Mordell, Diophantine Equations, Academic Press, 1969.
• [10] I. Niven and H. S. Zuckerman, An Introduction to the Theory of Numbers, Wiley, 1972.
• [11] P. Ribenboim, Catalan's Conjecture, Academic Press, 1994.
• [12] O. Rigge, Über ein diophantisches Problem, in: 9th Congress Math. Scand., Helsingfors, 1938, Mercator, 155-160.
• [13] J. B. Rosser and L. Schoenfeld, Approximate formulas for some functions of prime numbers, Illinois J. Math. 6 (1962), 64-94.
• [14] N. Saradha, On perfect powers in products with terms from arithmetic progressions, Acta Arith. 82 (1997), 147-172.
• [15] T. N. Shorey and R. Tijdeman, On the greatest prime factor of an arithmetical progression, in: A Tribute to Paul Erdős, A. Baker, B. Bollobás and A. Hajnal (eds.), Cambridge Univ. Press, 1990, 385-389.
• [16] T. N. Shorey and R. Tijdeman, Perfect powers in products of terms in an arithmetical progression, Compositio Math. 75 (1990), 307-344.
• [17] G. N. Watson, The problem of the square pyramid, Messenger Math. 48 (1919), 1-22.