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Cereceda, José Luis – International Journal of Mathematical Education in Science and Technology, 2020
In this paper, we first focus on the sum of powers of the first n positive odd integers, T[subscript k](n)=1[superscript k]+3[superscript k]+5[superscript k]+...+(2n-1)[superscript k], and derive in an elementary way a polynomial formula for T[subscript k](n) in terms of a specific type of generalized Stirling numbers. Then we consider the sum of…
Descriptors: Numbers, Arithmetic, Mathematical Formulas, Computation
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Pruitt, Kenny; Shannon, A. G. – International Journal of Mathematical Education in Science and Technology, 2018
The purpose of this paper is to consider analogues of the twin-prime conjecture in various classes within modular rings.
Descriptors: Mathematics Instruction, Numbers, Teaching Methods, Arithmetic
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Firozzaman, Firoz; Firoz, Fahim – International Journal of Mathematical Education in Science and Technology, 2017
Understanding the solution of a problem may require the reader to have background knowledge on the subject. For instance, finding an integer which, when divided by a nonzero integer leaves a remainder; but when divided by another nonzero integer may leave a different remainder. To find a smallest positive integer or a set of integers following the…
Descriptors: Mathematics Instruction, Numbers, Mathematical Concepts, Equations (Mathematics)
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Whitacre, Ian; Pierson Bishop, Jessica; Lamb, Lisa L.; Philipp, Randolph A.; Bagley, Spencer; Schappelle, Bonnie P. – International Journal of Mathematical Education in Science and Technology, 2015
We interviewed 40 students each in grades 7 and 11 to investigate their integer-related reasoning. In one task, the students were asked to write and interpret equations related to a story problem about borrowing money from a friend. All the students solved the story problem correctly. However, they reasoned about the problem in different ways.…
Descriptors: Grade 7, Grade 11, Interviews, Mathematical Logic
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Lynch, Mark A. M. – International Journal of Mathematical Education in Science and Technology, 2011
A procedure for generating quasigroups from groups is described, and the properties of these derived quasigroups are investigated. Some practical examples of the procedure and related results are presented.
Descriptors: Algebra, Mathematics, Mathematics Instruction, Mathematics Education
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Torres-Jimenez, Jose; Rangel-Valdez, Nelson; Gonzalez-Hernandez, Ana Loreto; Avila-George, Himer – International Journal of Mathematical Education in Science and Technology, 2011
A branch of mathematics commonly used in cryptography is Galois Fields GF(p[superscript n]). Two basic operations performed in GF(p[superscript n]) are the addition and the multiplication. While the addition is generally easy to compute, the multiplication requires a special treatment. A well-known method to compute the multiplication is based on…
Descriptors: Numbers, Mathematics Instruction, Tables (Data), Arithmetic
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Sprows, David J. – International Journal of Mathematical Education in Science and Technology, 2010
This note can be used to illustrate to the student such concepts as periodicity in the complex plane. The basic construction makes use of the Tent function which requires only that the student have some working knowledge of binary arithmetic.
Descriptors: Arithmetic, Intervals, Mathematics, Mathematical Formulas
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Shutler, Paul M. E.; Fong, Ng Swee – International Journal of Mathematical Education in Science and Technology, 2010
Modern Hindu-Arabic numeration is the end result of a long period of evolution, and is clearly superior to any system that has gone before, but is it optimal? We compare it to a hypothetical base 5 system, which we dub Predator arithmetic, and judge which of the two systems is superior from a mathematics education point of view. We find that…
Descriptors: Elementary School Mathematics, Mathematics Instruction, Computation, Arithmetic
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Coughlin, Heather; Jue, Brian – International Journal of Mathematical Education in Science and Technology, 2009
There is a very natural way to divide a four-digit number into 2 two-digit numbers. Applying an algorithm to this pair of numbers, determine how often the original four-digit number reappears. (Contains 3 tables.)
Descriptors: Numbers, Mathematics Instruction, Arithmetic, Equations (Mathematics)
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Abramovich, Sergei – International Journal of Mathematical Education in Science and Technology, 2012
This article explores the notion of collateral learning in the context of classic ideas about the summation of powers of the first "n" counting numbers. Proceeding from the well-known legend about young Gauss, this article demonstrates the value of reflection under the guidance of "the more knowledgeable other" as a pedagogical method of making…
Descriptors: Teaching Methods, Preservice Teacher Education, Learning Experience, Mathematics Education
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Plaza, A.; Falcon, S. – International Journal of Mathematical Education in Science and Technology, 2008
This note shows a combinatorial approach to some identities for generalized Fibonacci numbers. While it is a straightforward task to prove these identities with induction, and also by arithmetical manipulations such as rearrangements, the approach used here is quite simple to follow and eventually reduces the proof to a counting problem. (Contains…
Descriptors: Arithmetic, Mathematics Instruction, Problem Solving, Validity
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Ramasinghe, W. – International Journal of Mathematical Education in Science and Technology, 2007
It is well known that simple examples are really encouraging in the understanding of rearrangements of infinite series. In this paper a similar role is played by simple examples in the case of infinite products. Iterated products of double products seem to have a similar spirit of rearrangements of products, although they are not the same.…
Descriptors: Mathematics Instruction, Arithmetic, Mathematical Concepts, Numbers
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Asiru, Muniru A. – International Journal of Mathematical Education in Science and Technology, 2008
The note introduces sequences having M-bonacci property. Two summation formulas for sequences with M-bonacci property are derived. The formulas are generalizations of corresponding summation formulas for both M-bonacci numbers and Fibonacci numbers that have appeared previously in the literature. Applications to the Arithmetic series, "m"th "g -…
Descriptors: Validity, Mathematical Logic, Problem Solving, Numbers
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Duckworth, W. Ethan – International Journal of Mathematical Education in Science and Technology, 2008
This article provides a survey of some basic results in algebraic number theory and applies this material to prove that the cyclotomic integers generated by a seventh root of unity are a unique factorization domain. Part of the proof uses the computer algebra system Maple to find and verify factorizations. The proofs use a combination of historic…
Descriptors: Number Concepts, Algebra, Mathematics Instruction, Computer Uses in Education
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Plaza, A.; Falcon, S. – International Journal of Mathematical Education in Science and Technology, 2008
In this article, we consider some generalizations of Fibonacci numbers. We consider k-Fibonacci numbers (that follow the recurrence rule F[subscript k,n + 2] = kF[subscript k,n + 1] + F[subscript k,n]), the (k, l)-Fibonacci numbers (that follow the recurrence rule F[subscript k,n + 2] = kF[subscript k,n + 1] + lF[subscript k,n]), and the Fibonacci…
Descriptors: Numbers, Mathematical Concepts, Mathematics Instruction, Problem Solving
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