منابع مشابه
On 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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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
متن کاملOn Pillai’s Diophantine equation
Let A, B, a, b and c be fixed nonzero integers. We prove several results on the number of solutions to Pillai’s Diophantine equation Aa −Bby = c in positive unknown integers x and y.
متن کاملOn the Diophantine Equation
In this paper, we study the Diophantine equation x2 + C = 2yn in positive integers x, y with gcd(x, y) = 1, where n ≥ 3 and C is a positive integer. If C ≡ 1 (mod 4) we give a very sharp bound for prime values of the exponent n; our main tool here is the result on existence of primitive divisors in Lehmer sequence due Bilu, Hanrot and Voutier. When C 6≡ 1 (mod 4) we explain how the equation can...
متن کاملOn the Diophantine Equation
= c for some integers a, b, c with ab 6= 0, has only finitely many integer solutions. Stoll & Tichy proved more generally that if a, b, c ∈ Q and ab 6= 0, then for m > n ≥ 3, the above equation has only finitely many integral solutions x, y. Independently, Rakaczki established a more precise finiteness result on this binomial equation and extended this result to more general equations (see Acta...
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ژورنال
عنوان ژورنال: Proceedings of the Edinburgh Mathematical Society
سال: 1996
ISSN: 0013-0915,1464-3839
DOI: 10.1017/s0013091500022811