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SOLVING n(n plus d) . . . (n plus (k-1)d) = by(2) WITH P(b) <= Ck

Author:
Filaseta, M.  Laishram, S.  Saradha, N.  


Journal:
INTERNATIONAL JOURNAL OF NUMBER THEORY


Issue Date:
2012


Abstract(summary):

We examine the problem of determining the solutions to the Diophantine equation n(n + d) . . . (n + (k - 1)d) = by(2), where d is fixed and the largest prime divisor of b is no more than Ck. Here, C is fixed but arbitrary. Under some rather minor conditions, it is shown that there are finitely many solutions that can be effectively computed. Some new, largely combinatorial, ideas are introduced into the general theory to handle the case of arbitrary C as considered here.


Page:
161---173


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