Max–min of polynomials and exponential diophantine equations (II)
نویسندگان
چکیده
منابع مشابه
Exponential Diophantine Equations
1. Historical introduction. Many questions in number theory concern perfect powers, numbers of the form a b where a and b are rational integers with <7>1, 6>1. To mention a few: (a) Is it possible that for /zs>3 the sum of two 77th powers is an /7th power? (b) Is 8, 9 the only pair of perfect powers which differ by 1 ? (c) Is it possible that the product of consecutive integers, (x+l)(x + 2) .....
متن کاملIndecomposability of polynomials and related Diophantine equations
We present a new criterion for indecomposability of polynomials over Z. Using the criterion we obtain general finiteness result on polynomial Diophantine equation f(x) = g(y).
متن کاملClass Numbers, Quadratics, and Exponential Diophantine Equations
We look at the relationships between class numbers of quadratic structures (orders and fields) and the solutions of exponential Diophantine equations. We conclude with necessary and sufficient conditions for a class group to have an element of a given order. 1. Notation and Preliminaries If D is a squarefree integer, then its discriminant is given by ( ) ( ) ≡ ≡/ = ∆ . 4 mod 1 if , 4 mod ...
متن کاملOn a Conjecture on Exponential Diophantine Equations
We deal with a conjecture of Terai (1994) asserting that if a, b, c are fixed coprime integers with min(a, b, c) > 1 such that a+b = c for a certain odd integer r > 1, then the equation a + b = c has only one solution in positive integers with min(x, y, z) > 1. Co-operation man-machine is needed for the proof.
متن کاملOn Some Diophantine Equations (ii)
In [7] we have studied the equation m − n = py, where p is a prime natural number p ≥ 3. Using the above result, in this paper, we study the equations ck(x 4 + 6px y +py) + 4pdk(x y + pxy) = 32z with p ∈ {5, 13, 29, 37}, where (ck, dk) is a solution of the Pell equation ∣∣c2 − pd2∣∣ = 1.
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: 2015
ISSN: 0022-314X
DOI: 10.1016/j.jnt.2015.05.020