On the Diophantine equation $x\sp{p}+y\sp{p}=cz\sp{p}$
نویسندگان
چکیده
منابع مشابه
On 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...
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If a, b and n are positive integers with b ≥ a and n ≥ 3, then the equation of the title possesses at most one solution in positive integers x and y, with the possible exceptions of (a, b, n) satisfying b = a + 1, 2 ≤ a ≤ min{0.3n, 83} and 17 ≤ n ≤ 347. The proof of this result relies on a variety of diophantine approximation techniques including those of rational approximation to hypergeometri...
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ژورنال
عنوان ژورنال: Proceedings of the American Mathematical Society
سال: 1965
ISSN: 0002-9939
DOI: 10.1090/s0002-9939-1965-0180526-8