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On kth Power of Upper Bound Graphs
 ANNALS OF COMBINATORICS
, 2003
"... We consider kth power of upper bound graphs. According to the characterization of upper bound graphs, we obtain a characterization of kth power of upper bound graphs. That is, for a connected upper bound graph G; Gk is an upper bound graph if and only if for any pair of Aksimplicial vertices s1 ..."
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We consider kth power of upper bound graphs. According to the characterization of upper bound graphs, we obtain a characterization of kth power of upper bound graphs. That is, for a connected upper bound graph G; Gk is an upper bound graph if and only if for any pair of Aksimplicial vertices s
SUMS AND DIFFERENCES OF FOUR kTH POWERS
, 2009
"... We prove an upper bound for the number of representations of a positive integer N as the sum of four kth powers of integers of size at most B, using a new version of the Determinant method developed by HeathBrown, along with recent results by Salberger on the density of integral points on affine ..."
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We prove an upper bound for the number of representations of a positive integer N as the sum of four kth powers of integers of size at most B, using a new version of the Determinant method developed by HeathBrown, along with recent results by Salberger on the density of integral points
HARARY INDEX OF THE kTH POWER OF A GRAPH
 APPL. ANAL. DISCRETE MATH. 7 (2013), 94–105
, 2013
"... The kth power of a graph G, denoted by Gk, is a graph with the same set of vertices as G, such that two vertices are adjacent in Gk if and only if their distance in G is at most k. The Harary index H is the sum of the reciprocal distances of all pairs of vertices of the underlying graph. Lower and ..."
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Cited by 2 (0 self)
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The kth power of a graph G, denoted by Gk, is a graph with the same set of vertices as G, such that two vertices are adjacent in Gk if and only if their distance in G is at most k. The Harary index H is the sum of the reciprocal distances of all pairs of vertices of the underlying graph. Lower
The least kth power nonresidue
, 2011
"... Let p be a prime number and let k ≥ 2 be an integer such that k divides p − 1. Norton proved that the least kth power nonresidue modp is at most 3.9p 1/4 log p unless k = 2 and p ≡ 3 (mod 4), in which case the bound is 4.7p 1/4 log p. With a combinatorial idea and a little help from computing powe ..."
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Cited by 3 (3 self)
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Let p be a prime number and let k ≥ 2 be an integer such that k divides p − 1. Norton proved that the least kth power nonresidue modp is at most 3.9p 1/4 log p unless k = 2 and p ≡ 3 (mod 4), in which case the bound is 4.7p 1/4 log p. With a combinatorial idea and a little help from computing
Matrices over orders in algebraic number fields as sums of kth powers
 Proc. Amer. Math. Soc
"... Abstract. David R. Richman proved that for n ≥ k ≥ 2 every integral n × n matrix is a sum of seven kth powers. In this paper, in light of a question proposed earlier by M. Newman for the ring of integers of an algebraic number field, we obtain a discriminant criterion for every n × n matrix (n ≥ k ..."
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Cited by 2 (1 self)
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Abstract. David R. Richman proved that for n ≥ k ≥ 2 every integral n × n matrix is a sum of seven kth powers. In this paper, in light of a question proposed earlier by M. Newman for the ring of integers of an algebraic number field, we obtain a discriminant criterion for every n × n matrix (n ≥ k
On the 2kth power mean value of the generalized quadratic Gauss sum
 Bull Korean Math. Soc
"... Abstract. The main purpose of this paper is using the elementary and analytic methods to study the properties of the 2kth power mean value of the generalized quadratic Gauss sums, and give two exact mean value formulae for k = 3 and 4. 1. ..."
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Cited by 1 (0 self)
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Abstract. The main purpose of this paper is using the elementary and analytic methods to study the properties of the 2kth power mean value of the generalized quadratic Gauss sums, and give two exact mean value formulae for k = 3 and 4. 1.
ON kTHPOWER NUMERICAL CENTRES
"... Abstract. We call the integer N a kthpower numerical centre for n if ..."
Sums and Differences of Three kth Powers
"... If k ≥ 2 is a positive integer the number of representations of a positive integer N as either x k 1 + x k 2 = N or x k 1 − x k 2 = N, with integers x1 and x2, is finite. Moreover it is easily shown to be Oε(N ε), for any ε> 0. It is known that if k = 2 or 3 then the number of representations is ..."
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Cited by 7 (1 self)
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If k ≥ 2 is a positive integer the number of representations of a positive integer N as either x k 1 + x k 2 = N or x k 1 − x k 2 = N, with integers x1 and x2, is finite. Moreover it is easily shown to be Oε(N ε), for any ε> 0. It is known that if k = 2 or 3 then the number of representations
kTH POWER RESIDUE CHAINS OF GLOBAL FIELDS
, 907
"... Abstract. In 1974, Vegh proved that if k is a prime and m a positive integer, there is an m term permutation chain of kth power residue for infinitely many primes [E.Vegh, kth power residue chains, J.Number Theory, 9(1977), 179181]. In fact, his proof showed that 1, 2, 2 2,..., 2 m−1 is an m term p ..."
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Abstract. In 1974, Vegh proved that if k is a prime and m a positive integer, there is an m term permutation chain of kth power residue for infinitely many primes [E.Vegh, kth power residue chains, J.Number Theory, 9(1977), 179181]. In fact, his proof showed that 1, 2, 2 2,..., 2 m−1 is an m term
Results 1  10
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1,046