Results 121 to 130 of about 1,510,077 (175)

One hundred years of complex dynamics. [PDF]

Proc Math Phys Eng Sci, 2016
Rees M.
europepmc   +1 more source

Rational approximations to linear forms of exponentials and binomials. [PDF]

Proc Natl Acad Sci U S A, 1983
Chudnovsky GV.
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Solution of the Exponential Diophantine Equation

Journal of Chemical, Biological and physical sciences
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Some exponential Diophantine equations

, 1993
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Solutions for a Class of the Exponential Diophantine Equation

Advanced Materials Research, 2013
We studied the Diophantine equation x2+4n=y11. By using the elementary method and algebraic number theory, we obtain the following conclusions: (i) Let x be an odd number, one necessary condition which the equation has integer solutions is that 210n-1/11 contains some square factors.
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ON THE SOLUTION OF A CLASS OF EXPONENTIAL DIOPHANTINE EQUATIONS

South East Asian J. of Mathematics and Mathematical Sciences, 2022
In this note, we show that for n = 4N + 3, N     N      0  , the expo- nential Diophantine equation nx + 24y = z2 has exactly two solutions if n + 1 or equivalently N + 1 is an square. When N + 1 = m2, the solutions are given by (0, 1, 5) and (1, 0, 2m). Otherwise it has a unique solution (0, 1, 5) in non-negative integers.
Dutta, Mridul, Borah, Padma Bhushan
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An Exponential Diophantine Equation: 10873

The American Mathematical Monthly, 2003
Solution by Doyle Henderson, Omaha, NE. The only possibilities for m are 0, 1, 2, 3, and 5. Simple calculations then show the solution set for (m, n) to be {(0, 0), (1, 1), (2, 2), (5, 11)1}. Suppose there is a solution with m even and at least 4. Let m = 2a and x = 3a We have x2 2n2 = 1.
B. J. Venkatachala, Doyle Henderson
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ON THE EXPONENTIAL DIOPHANTINE EQUATION

Bulletin of the Australian Mathematical Society, 2014
AbstractLet$m$,$a$,$c$be positive integers with$a\equiv 3, 5~({\rm mod} \hspace{0.334em} 8)$. We show that when$1+ c= {a}^{2} $, the exponential Diophantine equation$\mathop{({m}^{2} + 1)}\nolimits ^{x} + \mathop{(c{m}^{2} - 1)}\nolimits ^{y} = \mathop{(am)}\nolimits ^{z} $has only the positive integer solution$(x, y, z)= (1, 1, 2)$under the condition ...
TAKAFUMI MIYAZAKI, NOBUHIRO TERAI
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