[PDF] Top 20 Positive Integers n Such That σ(φ(n)) = σ(n)
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Positive Integers n Such That σ(φ(n)) = σ(n)
... and if q > m is a Sophie Germain prime, that is a prime number q such that p = 2q + 1 is also prime, then n = mp ∈ A . The numbers m = 2318, 2806, 5734, 5937, 7198, 8097, . . . all satisfy relation (1), and ... See full document
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Some Central Limit Theorems for Doubly Restricted Partitions
... If K, L, and N are positive integers, the function PK,LN is define d to be the number of unordered partitions of N into K parts, the largest of For example, 22 has 11 partitions into 5 p[r] ... See full document
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Geometric Series of Numbers Approximating Positive Integers
... any positive integer value of ...a positive integer closer and closer as the series ...of n, that is not adjacent to a perfect square, neither is a perfect square, can be determined by finding the ... See full document
15
Mixing Time and Cutoff for a Random Walk on the Ring of Integers mod n
... O(ln n ln ln n) can be obtained for the mixing time of X by employing the method of Chung et ...then n/σ S ′ = O(1), and thus T n is ... See full document
16
On the Diophantine equation Ax2+22m=yn
... that n > 2 is an odd integer with (n,h) = 1 and m > ...in positive integers x and y if n has any prime factor congruent to 1 modulo ...If n has no such factor it is proved ... See full document
9
Mixing Time and Cutoff for a Random Walk on the Ring of Integers mod n
... 2 n, and an upper bound of O(log 2 n log 2 log 2 n) can be obtained by employing the method of Chung et ...then n/σ S ′ = O(1), and ... See full document
12
Prime divisors of some shifted products
... of positive integers A(n) + 1, n = 1, . . .,N, such that the ratios a(n) = A(n)/A(n − 1) have some number-theoretic or combinatorial ...= n, we obviously ... See full document
17
Mathematical Induction I.pptx
... all positive integers n, where P(n) is a propositional ...“if n is a positive integer, then n 3 − n is divisible by 3” is an example of ... See full document
26
Some Results on the Derivatives of the Gamma and Incomplete Gamma Function for Non-positive Integers
... in Theorem 4 and 5 in [2], respectively. Furthermore, the corresponding corrections have been given in Remark 2.4 and 2.5, respectively. Finally, Γ (n) ( − m, z) are represented as the combination of Γ (j) (1, ... See full document
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#A12 INTEGERS 13 (2013) THE DISTRIBUTION OF SOLUTIONS TO XY = N (MOD A) WITH AN APPLICATION TO FACTORING INTEGERS
... evaluate N mod a − δ for d + 1 values of ...values positive, we consider non-negative values of δ, and, for good measure, take extra values, δ = 0, 1, 2, ... See full document
20
Certain near rings are rings, II
... elements of R which do not commute; and let m, n, s, t be positive integers, at least I, then If ns bma n anSb one of which is greater than I, for which ab mt mt-I abmt v If ns > I, then[r] ... See full document
6
Coefficient subrings of certain local rings with prime power characteristic
... For any positive integers n and r, there exists up to isomorphism a unique r-dimensional separable extension GRp",r of Z/p"Z, which is called the Galois ring of characteristic.. This rin[r] ... See full document
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Counting Techniques -II.pptx
... with n elements can be placed in one-to-one correspondence with the set {1, 2, 3, ..., n}. We can list the permutations of any set of n elements by generating the permutations of the n ... See full document
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On \(\frac{1}{w} + \frac{1}{x} + \frac{1}{y} + \frac{1}{z} = \frac{1}{ 2} \) and some of its generalizations
... In this paper, we give a straightforward approach to obtaining the solution of the Diophantine equation w 1 + 1 x + 1 y + 1 z = 1 2 . We also establish that the Diophantine equation w 1 + 1 x + 1 y + 1 z = m n for ... See full document
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On the number of representations of positive integers by quadratic forms as the basis of the space S4(Γ0(47),1)
... The number of representations of positive integers by quadratic forms F 1 = x 1 2 + x 1 x 2 + 12x 2 2 and G 1 = 3x 1 2 +x 1 x 2 + 4x 2 2 of discriminant −47 are given. Moreover, a basis for the space S 4 (Γ ... See full document
10
Arithmetic Progression Graphs
... of positive integers with n terms, is it possible to find an edge labeled graph with n vertices such that the se- quence of the sums of incident edges of its vertices produces the same ... See full document
8
Constructing a Subsequence of (Exp(in))n∈N Converging towards Exp(iα) for a Given α∈R
... of positive integers such that by applying the functions sin and cos we obtain two convergent se- quences with prescribed limits in the interval [ − 1,1 ] ...) n , n ∈ , are dense in [ ] 0,1 ... See full document
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Algebra/Geometry Institute Summer 2007 Susan Theunissen T. R. Sanders Elementary/Hollandale
... Teacher will observe students using counters to add positive and negative integers. Teacher will ask questions and respond to answers while students are adding positive and negative int[r] ... See full document
7
Effect of Plasticizer and Lithium Salt Concentration in PMMA-based Composite Polymer Electrolytes
... ln σ versus 1/T plots of these polymer electrolytes, some observed temperature dependence of ln σ versus 1/T are not linear but polynomial (n = 2 or n = 3), and the conductivity of polymer ... See full document
15
Small Area Estimation Under Informative Sampling
... x = β µ = . Note that under the model (6.1) and the sampling scheme used to select the areas, the sample random effects also have a normal distribution but with a different expectation, thus justifying the use of the ... See full document
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