Questions tagged [integer]

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1answer
64 views

Extending NumberForm

I'd like to define a function, call it NumberF, that takes a real number n and two naturals l...
3
votes
3answers
154 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{...
4
votes
1answer
142 views

Representing number domain by a symbol [closed]

I'd like to represent the number domain by a symbol rather than text word. While Solve[n^2 - 19 n + 99 == k^2 \[And] {k, n} > 0, {k, n}, Integers] works fine, I'...
5
votes
2answers
416 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, ...
6
votes
1answer
72 views

Convert ByteArray to integer and real values

during the import of a complex file format I handle ByteArray or lists of byte values. While I can easy transform them from one type to each other: ...