Questions tagged [integer]

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Integer parameter assumption gives incorrect result when integrating

There are some dangerous pitfalls that can happen when evaluating some integrals, assuming that some parameters are integers. For example, consider the following: ...
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3 votes
1 answer
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What is the fastest way to check whether a cubic equation is solvable in integers?

My code needs to check whether a lot of low-degree equations (usually quadratic and cubic) are solvable in integers. There are many equations, so the speed is crucial. Let us start with quadratic ...
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3 votes
1 answer
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Choosing numbers whose divisors can be partitioned into subsets having the equal sum

How can we find the list of natural numbers between 100 to 10000, whose positive divisors can be partitioned into three subsets such that sum of all the elements in three subsets will be equal?
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4 votes
1 answer
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Choosing a subset of a set based on the sum of its elements

How can we choose a subset of a set based on the sum of the elements of the subset? For instance, n=6 dn=Divisors[n] sn=DivisorSum[n,#&] Is it possible to ...
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2 votes
2 answers
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making elements of matrix into integers [closed]

how to make elements in a matrix into integers? here is my matrix: ...
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1 vote
3 answers
145 views

Help me plot this function [closed]

f[k] = -(1/2)^k - ((1/4) (1 - sqrt[5]))^k/sqrt[5] + ((1/4) (1 + sqrt[5]))^k/sqrt[5] (and also f[k] = 0 when k = 1,2) I need to make a lineplot of this function in k = 3,4,5,... ,20. why this does not ...
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  • 135
1 vote
2 answers
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InputField : only integer or list of integers in a specific range

I'm making a dynamic structure which reads some output from a FEM program (node results). I'd like an inputfield in which I specify the number(s) of the nodes I am interested in. The value of the ...
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1 vote
1 answer
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Extending NumberForm

I'd like to define a function, call it NumberF, that takes a real number n and two naturals l...
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  • 4,138
3 votes
3 answers
162 views

Show that all coefficients in a recursively defined function are integers

Problem 2 in the 2017 Putnam exam is: Let $Q_0(x) = 1$, $Q_1(x) = x$, and $Q_n(x) = \frac{Q_{n-1}^2(x) - 1}{Q_{n-2}(x)}$. Show that $Q_n(x) \in \mathbb{Z}[x]\ \forall n \geq 0$. (Recall that $\mathbb{...
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5 votes
2 answers
442 views

Solving an equation over the integers

Consider the problem of finding all values of $n \in \mathbb{N}$ s.t. $$\sqrt{n} + \sqrt{n + 2005}$$ is an integer. One can easily verify that $n = 1,004,004$ and $39,204$ satisfy this requirement, ...
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3 votes
1 answer
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Testing that an expression resolves to an integer [closed]

As shown in this video, the expression $$4 \sqrt{4 - 2 \sqrt{3}} + \sqrt{97 - 56 \sqrt{3}}$$ is in fact an integer. One way to check is: ...
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