منابع مشابه
On the Exponential Diophantine Equation
Let a, b, c be fixed positive integers satisfying a2 + ab + b2 = c with gcd(a, b) = 1. We show that the Diophantine equation a2x+axby+b2y = cz has only the positive integer solution (x, y, z) = (1, 1, 1) under some conditions. The proof is based on elementary methods and Cohn’s ones concerning the Diophantine equation x2 + C = yn. Mathematics Subject Classification: 11D61
متن کاملThe Exponential Diophantine Equation 2x + by = cz
Let b and c be fixed coprime odd positive integers with min{b, c} > 1. In this paper, a classification of all positive integer solutions (x, y, z) of the equation 2 (x) + b (y) = c (z) is given. Further, by an elementary approach, we prove that if c = b + 2, then the equation has only the positive integer solution (x, y, z) = (1,1, 1), except for (b, x, y, z) = (89,13,1, 2) and (2 (r) - 1, r + ...
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Let m be a positive integer. Then we show that the exponential Diophantine equation (4m2 + 1)x + (5m2 − 1)y = (3m)z has only the positive integer solution (x, y, z) = (1, 1, 2) under some conditions. The proof is based on elementary methods and Baker’s method. Mathematics Subject Classification: 11D61
متن کاملExponential 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 کاملAn Exponential Martingale Equation
We prove an existence of a unique solution of an exponential martingale equation in the class of BMO martingales. The solution is used to characterize optimal martingale measures.
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ژورنال
عنوان ژورنال: Bulletin of the Australian Mathematical Society
سال: 2001
ISSN: 0004-9727,1755-1633
DOI: 10.1017/s0004972700019717