# Tagged Questions

**3**

votes

**1**answer

260 views

### Sequences with integral variances

This is a companion to my earlier question,
Sequences with integral means.
This new question is, frankly, not as interesting, but it feels necessary to complete
the thought.
Let $V(n)$ be the ...

**20**

votes

**5**answers

637 views

### Sequences with integral means

Let $S(n)$ be the sequence whose first element is $n$, and from then onward,
the next element is the smallest natural number ${\ge}1$ that ensures that the
mean of all the numbers in the sequence is ...

**6**

votes

**3**answers

536 views

### References on techniques for solving equations with discontinuous functions such as floor and ceiling?

Here I describe the sort of reference I'm after with a motivating example. I am not seeking solutions to my equations on this forum; I'm quite happy to do that myself. Rather, I'm asking for some good ...

**5**

votes

**0**answers

414 views

### Optimal Gear Trains

Suppose you need to slow down a turning motor so that a gear turns at
an angular velocity $\frac{a}{b}$ of that of the motor shaft, where $a$ and
$b$ are natural numbers. For example, this set of ...

**5**

votes

**2**answers

242 views

### Lattice-cube minimal blocking sets

Let $C_d(n)$ be the lattice cube consisting of the $n^d$ points with
each of its $d$ coorindates in $\lbrace 1,2,\ldots,n \rbrace$.
Define a blocking set for a lattice cube to be a set of points
in ...

**12**

votes

**5**answers

1k views

### Special arithmetic progressions involving perfect squares

Some time ago the following rather easy problem appeared in an online publication called "Problems in Elementary NT" by Hojoo Lee:
Prove that there are infinitely many positive integers $a$, $b$, $c$ ...

**13**

votes

**3**answers

782 views

### Partitioning the integers $1$ through $n$ so that the product of the elements in one set is equal to the sum of the elements in the other

I asked this question at math.SE a couple of months ago and only got a partial answer, so I thought I would try here.
It is known that, for $n \geq 5$, it is possible to partition the integers ...