منابع مشابه
On a Diophantine Equation
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 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...
متن کاملOn the inverse Fermat equation
Lenstra Jr, H.W., On the inverse Fermat equation, Discrete Mathematics 106/107 (1992) 329-33 1. In this paper the equation x”” + y”” = z “n is solved in positive integers x, y, z, n. If the nth roots are taken to be positive real numbers, then all solutions are known to be trivial in a certain sense. A very short proof of this is provided. The argument extends to give a complete description of ...
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 کاملذخیره در منابع من
با ذخیره ی این منبع در منابع من، دسترسی به آن را برای استفاده های بعدی آسان تر کنید
ژورنال
عنوان ژورنال: Journal of Number Theory
سال: 2000
ISSN: 0022-314X
DOI: 10.1006/jnth.1999.2438