Questions tagged [number-theory]
For questions related to the teaching of number theory, the part of mathematics concerned with properties of the positive integers.
50 questions
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How to effectively teach primitive roots and quadratic residues without assuming prior knowledge of abstract algebra?
I have been teaching Number Theory to undergraduate students. Topics such as divisibility, primes, congruences, and basic Diophantine equations were well-received and seemed to engage the class ...
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Which is better/correct ? no remainder or remainder zero?
From didactic, linguistic, and mathematical perspectives, which is more correct to write: "The division of 4 by 2 leaves no remainder" or "The division of 4 by 2 leaves a remainder of ...
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Is Induction implied within Definition of Recursion? [closed]
Hi I was reading about definition of Addition:
n + 0 = n
n + S(m) = S(n + m)
Between these two above mentioned steps, moving ...
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Resources to introduce Modular arithmetic
We have Clock arithmetic in grades 5 , 6 and thereafter nothing related to the Modular arithmetic is taught until students enter to the universities. Since this is very important topic in Number ...
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Limitations of applying the factor theorem
Here are three situations in which students might try to apply the factor theorem.
Proving that $x + 1$ is a factor of the polynomial $x^3 + x + 2$ can be done using the factor theorem by showing ...
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Whole numbers as sets vs abstracted properties of sets
I recently landed on a book written for elementary school teachers which introduced the concept of whole numbers in the following manner:
We have a set $\{\alpha, \beta, \gamma\}$. There are other ...
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congruency: how widely used?
Today I was made aware of the term "congruency" as a word related to congruence in the same way that equality is related to equation. I have never seen the term "congruency" used ...
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What is the terminology for integers with the same oddness or evenness?
If two integers are either both negative or both positive, we can say they have the same sign.
How about two integers that are either both odd or both even? Is there any term for them?
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Reference request: an introduction to triangular, square, and other figurate numbers
There are dozens (maybe thousands) of websites that explain what triangular numbers, square numbers, etc. are. I'm searching for a printed book that includes this material, preferably at a level that ...
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Are there any mathematics based game apps which require students (between 10 - 16 years) to apply their maths knowledge to play the game
So, what we essentially mean is students will apply their knowledge on divisibility, factorization, prime numbers, lcm, gcf, decimals, fractions, etc to play the game. A somewhat different approach to ...
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Which academic subjects examine what the advantages and disadvantages of the various number bases are?
Which academic subjects examine what the advantages and disadvantages of the various number bases are, e.g. besides base ten: base twelve, base sixteen, base eight, base two and the ways that they can ...
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Why do we write numbers with decreasing place values?
This question came up while teaching ~16 year olds binary numbers. Why do place values increase to the left and not the other way round?
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Number theory in an introductory course on discrete dynamical systems
Benjamin Hutz, in Chapter 10 of his An Experimental Introduction to Number Theory, allows for the optional inclusion of discrete dynamical systems with a number-theoretic flavor in an undergraduate ...
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How can I explain construction of the Bézout's identity to my kid?
My kid is soon 7 years old, he could understand fractions, linear equation and modulo operation. I've just taught him Chinese remainder theorem, looking to introduce some more basic number theory ...
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Introductory book or other resource on $p$-adic numbers/number theory/analysis
I am having problems understanding $p$-adic numbers/$p$-adic number theory/$p$-adic analysis. I have tried some notes on the internet, but these notes were not helpful.
Can anyone suggest a book, ...
