Questions tagged [number-theory]
Questions on the number-theoretic functionality of Mathematica.
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When and how CoprimeQ[a, b, c] is evaluated for generic a, b, c? [closed]
Most Mathematica functions return input sentence unevaluated, when there is no simple solution, or, the answer cannot be determined from the input data. For example,
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Finding primes, so that the given eta product is hecke eigenform
I'm trying to write a code on mathematica which detects the prime numbers, p, for which the user given eta product is a hecke eigenform for that hecke operator T_p.
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How to generate lattice by integrating over curves on a modular form domain plot?
I was watching this video (2:30 of https://youtu.be/zLEyIT_BCgk?si=ji5NyjR7vcwzaNxi ).
Here in the video he said that to get the lattice , we just integrate over the curve(silver line) and we will ...
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Taxicab Geometry
According to taxicab geometry, there are 1226 possible paths from A(2,5) to B(7,9), all with a distance of 9 units, |2-7|+|9-5|=9. I wanted to write a code where I could be obtaining the plots of some ...
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Are there other methods to list the coprime arrays within the array? [duplicate]
The list array is:
list = Subsets[Range[2, 8], {2}]
get the list is:
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Mathematica code to compute a constant
I am reading an interesting paper One of the numbers ζ(5), ζ(7), ζ(9), ζ(11) is irrational by Zudilin. We fix odd numbers $q$ and $r$, $q\geq r+4$ and a tuple $\eta_0,\eta_1,...,\eta_q$ of positive ...
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Generation of rational numbers under constraints
Working this question on Mathematics Stack Exchange, I have the following questions:
how to generate a rational number $a$ such that $\sqrt{a^2-1}$ be also rational? This is the case of $a=\frac 54$.
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How to check if multiplication requires carries?
For some purposes I need to know if there are there any carries in the multiplication of two numbers, especially in base-2.
How can we do this in Mathematica?
Thanks
to all, very interesting answers!
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PrimeZetaP evaluation in different versions of Mathematica
PrimeZetaP was introduced in version 7.0. I suspect there were made some changes in the definition of this function in subsequent versions.
Is there any user that ...
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How to find value of variables so that my expression to be perfect squares?
Suppose I have the expression
$$\sqrt{p(2-p)} \tag 1$$
and the expression
$$
\sqrt{\frac{1}{4}\left( p-2 \right) ^2-\frac{4\left( p-1 \right) ^4}{\left( p-2 \right) ^2}}. \tag 2
$$
The Mathematica ...
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PartitionsP for non-integer arguments [closed]
Is there a reason why the function PartitionsP[] does not return anything for non-integer arguments, although there is a way to calculate using Rademacher’s ‘exact’ ...
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Does a(a+1)(a+2)-1=b²+2=10c+3 have solutions over natural numbers? If yes, how many?
It is a question from the math olympiad I was participating in that happened like a month ago. The provided solution turned out to be wrong.
It isn't the question itself, but the solution basically ...
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Digits of Pi in colored spiral
In How to make the digits of π go around in a spiral like this?
it is described how to plot pi in a spiralform (in my case as binary number):
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Select a subset in the bit-strings with even 1s overlapped - thank you
Model 1
Consider the permutation list of 4-bit-strings:
list = Permutations[{0, 0, 1, 1}, {4}]
which outputs:
{{0, 0, 1, 1}, {0, 1, 0, 1}, {0, 1, 1, 0}, {1, 0, 0, ...
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Better code for Ramsey partitions
Ramsey partitions for parameters $a$ and $b$ are certain integer partition of $a+b$ developed by McAvaney, Robertson, and Webb (Combinatorica 1992) for applications in fair division problems where two ...
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