Relevant bibliographies by topics / Consecutive powers (Algebra)

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Academic literature on the topic 'Consecutive powers (Algebra)'

Author: Grafiati
Published: 4 June 2021
Last updated: 31 January 2023

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Journal articles on the topic "Consecutive powers (Algebra)"

1

Mollin, R., and H. Williams. "Consecutive powers in continued fractions." Acta Arithmetica 61, no. 3 (1992): 233–64. http://dx.doi.org/10.4064/aa-61-3-233-264.

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2

Hanrot, G., N. Saradha, and T. N. Shorey. "Almost perfect powers in consecutive integers." Acta Arithmetica 99, no. 1 (2001): 13–25. http://dx.doi.org/10.4064/aa99-1-2.

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3

Rönnefarth, Helmuth. "On the differences of the consecutive powers of Banach algebra elements." Banach Center Publications 38, no. 1 (1997): 297–314. http://dx.doi.org/10.4064/-38-1-297-314.

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4

De Schutter, Bart, and Bart De Moor. "On the Sequence of Consecutive Powers of a Matrix in a Boolean Algebra." SIAM Journal on Matrix Analysis and Applications 21, no. 1 (1999): 328–54. http://dx.doi.org/10.1137/s0895479897326079.

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5

Shorey, T., and Yu Nesterenko. "Perfect powers in products of integers from a block of consecutive integers (II)." Acta Arithmetica 76, no. 2 (1996): 191–98. http://dx.doi.org/10.4064/aa-76-2-191-198.

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6

Pang, Chin-Tzong, and Sy-Ming Guu. "A note on the sequence of consecutive powers of a nonnegative matrix in max algebra." Linear Algebra and its Applications 330, no. 1-3 (2001): 209–13. http://dx.doi.org/10.1016/s0024-3795(01)00253-1.

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7

Choudhry, Ajai. "An improvement of Prouhet’s 1851 result on multigrade chains." International Journal of Number Theory 16, no. 07 (2020): 1425–32. http://dx.doi.org/10.1142/s179304212050075x.

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In 1851, Prouhet showed that when [Formula: see text] where [Formula: see text] and [Formula: see text] are positive integers, [Formula: see text], the first [Formula: see text] consecutive positive integers can be separated into [Formula: see text] sets, each set containing [Formula: see text] integers, such that the sum of the [Formula: see text]th powers of the members of each set is the same for [Formula: see text]. In this paper, we show that even when [Formula: see text] has the much smaller value [Formula: see text], the first [Formula: see text] consecutive positive integers can be separated into [Formula: see text] sets, each set containing [Formula: see text] integers, such that the integers of each set have equal sums of [Formula: see text]th powers for [Formula: see text]. Moreover, we show that this can be done in at least [Formula: see text] ways. We also show that there are infinitely many other positive integers [Formula: see text] such that the first [Formula: see text] consecutive positive integers can similarly be separated into [Formula: see text] sets of integers, each set containing [Formula: see text] integers, with equal sums of [Formula: see text]th powers for [Formula: see text], with the value of [Formula: see text] depending on the integer [Formula: see text].
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8

Skałba, M. "Products of disjoint blocks of integers being high powers." International Journal of Number Theory 15, no. 01 (2019): 85–88. http://dx.doi.org/10.1142/s1793042118501749.

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Fix [Formula: see text] and put [Formula: see text]. Improving on results of [M. Skałba, Products of disjoint blocks of consecutive integers which are powers, Colloq. Math. 98 (2003) 1–3], we prove the following. For a given [Formula: see text] and each [Formula: see text], there exists [Formula: see text] such that for any exponent [Formula: see text], there exist nonnegative integers [Formula: see text] satisfying the equation [Formula: see text] and inequalities: [Formula: see text] and [Formula: see text] with [Formula: see text]
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9

Schutter, Bart De. "On the ultimate behavior of the sequence of consecutive powers of a matrix in the max-plus algebra." Linear Algebra and its Applications 307, no. 1-3 (2000): 103–17. http://dx.doi.org/10.1016/s0024-3795(00)00013-6.

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10

Chen, Yong-Gao. "Five consecutive positive odd numbers, none of which can be expressed as a sum of two prime powers." Mathematics of Computation 74, no. 250 (2004): 1025–32. http://dx.doi.org/10.1090/s0025-5718-04-01674-6.

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Books on the topic "Consecutive powers (Algebra)"

1

Ribenboim, Paulo. Catalan's conjecture: Are 8 and 9 the only consecutive powers? Academic Press, 1994.

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2

The Problem of Catalan. Springer, 2014.

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3

Bugeaud, Yann, Maurice Mignotte, and Yuri F. Bilu. Problem of Catalan. Springer London, Limited, 2014.

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4

Russell, Susan Jo, Virginia Bastable, and Deborah Schifter. Number and Operations, Part 1: Building A System of Tens Casebook. National Council of Teachers of Mathematics, 2016.

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Conference papers on the topic "Consecutive powers (Algebra)"

1

SCHUTTER, B. DE, and B. DE MOOR. "ON THE SEQUENCE OF CONSECUTIVE MATRIX POWERS OF BOOLEAN MATRICES IN THE MAX-PLUS ALGEBRA." In Proceedings of the 6th IEEE Mediterranean Conference. WORLD SCIENTIFIC, 1999. http://dx.doi.org/10.1142/9789814447317_0111.

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