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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In this note, we mainly obtain the equation x2m − yn = z2 have finite positive integer solutions (x, y, z,m, n) satisfying x > y be two consecutive primes. Mathematics Subject Classification: 11A41; 11D41
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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.
متن کاملHow to Solve a Diophantine Equation
These notes represent an extended version of a talk I gave for the participants of the IMO 2009 and other interested people. We introduce diophantine equations and show evidence that it can be hard to solve them. Then we demonstrate how one can solve a specific equation related to numbers occurring several times in Pascal’s Triangle with state-of-the-art methods. 1. Diophantine Equations The to...
متن کاملOn a Quartic Diophantine Equation
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: LMS Journal of Computation and Mathematics
سال: 2005
ISSN: 1461-1570
DOI: 10.1112/s1461157000000929