منابع مشابه
A Binomial Diophantine Equation
following result. THEOREM 1. The only (n,m)eZ with n^2 and m5=4 satisfying © = ( 7 ) a r e {n> m)=(2> 4)> (6> 6)> and (21> Our binomial diophantine equation represents an elliptic curve, since it can be rewritten as a quartic polynomial being a square. Indeed, on putting u = 2/i 1 and v = 2m 3, we see at once that Theorem 1 follows from the following result. THEOREM 2. The only (u, v) e Z with ...
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The complete sets of solutions of the equation (n k ) = (m ` ) are determined for the cases (k, `) = (2, 3), (2, 4), (2, 6), (2, 8), (3, 4), (3, 6), (4, 6), (4, 8). In each of these cases the equation is reduced to an elliptic equation, which is solved by using linear forms in elliptic logarithms. In all but one case this is more or less routine, but in the remaining case ((k, `) = (3, 6)) we h...
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In this paper we study the Diophantine equation x −6xy +5y = 16Fn−1Fn+1, where (Fn) n≥0 is the Fibonacci sequence and we find a class of such equations having solutions which are determined.
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The wish to determine the complete set of rational integral solutions of (1) was expressed by Diaconis and Graham in [2, p. 328]. Apparently, the solutions to this diophantine problem correspond to values of keN for which the Radon transform based on the set of all xeZ\ with exactly four ones is not invertible. We thank Hendrik Lenstra who communicated the problem to Jaap Top, to whom we are eq...
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ژورنال
عنوان ژورنال: The Quarterly Journal of Mathematics
سال: 1996
ISSN: 0033-5606,1464-3847
DOI: 10.1093/qmath/47.2.221