Popular Values of Euler's Function
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منابع مشابه
A Measure of the Nonmonotonicity of the Euler Phi Function
ure of the nonmonotonicity of f. In particular, F is identically zero if and only if f is strictly increasing . Here we shall take f to be (p, Euler's function, and study the associated function F 4„ which we henceforth call F. We shall show that F(n)/n is asymptotically representable as a function of T(n)/n . Then we shall prove that F(n)/n has a distribution function. We shall study max,,, F(...
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A generalized Euler's totient is defined as a Dirichlet convolution of a power function and a product of the Souriau-Hsu-M ¨ obius function with a completely multiplicative function. Two combinatorial aspects of the generalized Euler's totient, namely, its connections to other totients and its relations with counting formulae, are investigated.
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The double zeta function was first studied by Euler in response to a letter from Goldbach in 1742. One of Euler’s results for this function is a decomposition formula, which expresses the product of two values of the Riemann zeta function as a finite sum of double zeta values involving binomial coefficients. Here, we establish a q-analog of Euler’s decomposition formula. More specifically, we s...
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then it is known, MacNeish [16] and Mann [17] that there exists a set of at least n(v) mutually orthogonal Latin squares (m.o.l.s.) of order v. It seemed plausible that n(v) is also the maximum possible number of m.o.l.s. of order v. This would have implied the correctness of Euler's [13] conjecture about the nonexistence of two orthogonal Latin squares of order v when v = 2 (mod 4), since n(v)...
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MacNeish's conjecture was disproved by Parker (12) who showed that in certain cases N(v) > n(v) by proving that if there exists a balanced incomplete block (BIB) design with v treatments, A = 1, and block size k which is a prime power then N(v) > k — 2, and that this result can be improved to N(v) > k — 1, when the design is symmetric and cyclic. Parker's result though it did not disprove Euler...
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