On the solvability of the equation and its application
Authors:
Qi Sun and Da Qing Wan
Journal:
Proc. Amer. Math. Soc. 100 (1987), 220224
MSC:
Primary 11D04
MathSciNet review:
884454
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Abstract: In this paper, we obtain a necessary and sufficient condition under which the equation of the title is unsolvable. More precisely, for the equation where are fixed positive integers, we prove the following result: The above equation is unsolvable if and only if 1. For some , or 2. If is the set of all even integers among , then are pairwise prime, and is prime to any odd number in .
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Sun Qi, Wan Daqing and Ma Degang, On the equation , Chinese Ann. of Math. (to appear).
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 R. J. Evans, On blocks of consecutive integers, Amer. Math. Monthly 76 (1969), 4849. MR 1535230
 [2]
 J. R. Joly, Nombre de solutions de certaines équations diagonales sur un corps fini, C. R. Acad. Sci. Paris Ser. AB 272 (1971), 15491552. MR 0282949 (44:183)
 [3]
 R. Kidl and H. Niederreiter, Finite fields, Encyclopedia of Math. and Its Appl., vol. 20, AddisonWesley, Reading, Mass, 1983.
 [4]
 W. M. Schmidt, Equations over finite fields, Lecture Notes in Math., vol. 536, SpringerVerlag, Berlin and New York, 1976. MR 0429733 (55:2744)
 [5]
 C. Small, Diagonal equations over large finite fields, Canad. J. Math. 36 (1984), 249262. MR 749983 (86e:11094)
 [6]
 Sun Qi, Wan Daqing and Ma Degang, On the equation , Chinese Ann. of Math. (to appear).
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Additional Information
DOI:
http://dx.doi.org/10.1090/S00029939198708844546
PII:
S 00029939(1987)08844546
Article copyright:
© Copyright 1987
American Mathematical Society
