The Consecutive Integer Game

2002 ◽  
Vol 75 (2) ◽  
pp. 123
Author(s):  
David M. Clark
Keyword(s):  
Consecutive Integer

The Consecutive Integer Game

2002 ◽  
Vol 75 (2) ◽  
pp. 123-129
Author(s):  
David M. Clark
Keyword(s):  
Consecutive Integer

scholarly journals Antibandwidth of a Graph

2012 ◽  
Vol 11 (4) ◽  
pp. 59-64
Author(s):  
Aditya Shastry ◽  
Nidhi Khandelwal
Keyword(s):  
Np Hard ◽  
Consecutive Integer ◽  
Connected Graphs ◽  
Integer Points ◽  
Exterior Boundary ◽  
Interior Boundary

The antibandwidth problem consists of placing the vertices of a graph on a line in consecutive integer points in such a way that the minimum difference of adjacent vertices is maximized. This problem is NP- hard. In this paper, we find some bounds for antibandwidth using some invariants of graphs. We prove that considerating the interior boundary and the exterior boundary when estimating the antibandwidth of connected graphs gives the same results.

Powerful numbers in the product of consecutive integer values of a polynomial

2019 ◽  
Vol 94 (3-4) ◽  
pp. 319-336 ◽  
Author(s):  
Pallab Kanti Dey ◽  
Shanta Laishram
Keyword(s):  
Consecutive Integer ◽  
Powerful Numbers

scholarly journals Reflective Conversation and Knowledge Development in Pre-service Teachers: The Case of Mathematical Generalization

2020 ◽  
Vol 9 (1) ◽  
pp. 40-62
Author(s):  
Eddie Aparicio Landa ◽  
Landy Sosa Moguel ◽  
Guadalupe Cabañas-Sánchez
Keyword(s):  
Mathematics Teachers ◽  
Professional Knowledge ◽  
Point Of View ◽  
Knowledge Development ◽  
Consecutive Integer ◽  
Mathematical Concepts ◽  
Mathematical Generalization ◽  
Reflective Conversation ◽  
Mathematics Course

This article examines the development of professional knowledge in pre-service mathematics teachers. From the discussion of a task associated with the multiplication of consecutive integer numbers, generalization is recognized as a process that allows to explore, to explain, and to validate mathematical results, and as an essential ability to develop in the teaching of arithmetic, algebra, and geometry by using various representations. The study was conducted during three sessions of a didactic mathematics course, in which the instructor and ten students participated. The conversations of each session were recorded on audio and video. It was found that the reflective conversation fosters this knowledge from questions about the nature and processes of construction of mathematical concepts from a mathematical and didactic point of view.

Proof Without Words: The Difference of Consecutive Integer Cubes Is Congruent to 1 Modulo 6

2014 ◽  
Vol 45 (2) ◽  
pp. 135-135
Author(s):  
Claudi Alsina ◽  
Roger Nelsen ◽  
Hasan Unal
Keyword(s):  
Consecutive Integer ◽  
The Difference

scholarly journals Diophantine equations of Erdös-Moser type

1996 ◽  
Vol 53 (2) ◽  
pp. 281-292 ◽  
Author(s):  
Pieter Moree
Keyword(s):  
Diophantine Equation ◽  
Diophantine Equations ◽  
Consecutive Integer ◽  
Elementary Method ◽  
Integer Solutions

Using an old result of Von Staudt on sums of consecutive integer powers, we shall show by an elementary method that the Diophantine equation 1k + 2k + … + (x − l)k = axk has no solutions (a, x, k) with k > 1, . For a = 1 this equation reduces to the Erdös-Moser equation and the result to a result of Moser. Our method can also be used to deal with variants of the equation of the title, and two examples will be given. For one of them there are no integer solutions with

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