Volume 54
, Issue 1

2018

Dear Readers, welcome to this year’s first issue of Parabola!
In this issue, you can find three excellent articles, David Angell’s beautifully set problems, and more of Robert Schneider’s hilarious comics strips $2\mathbb{Z}$ Or Not $2\mathbb{Z}$ which also offer the occasional cryptic puzzle.

Communication is no longer private, but rather a publicly broadcast signal for the entire world to overhear. Cryptography has taken on the responsibility of securing our private information.

This paper describes when given polynomials $z^n + z^k + z^j - 1$ have a unimodular root.

The terminating sum $T(n)$ of a positive integer $n$ is obtained by repeatedly adding the digits of $n$ until a single digit number is obtained.

An odd comic about even numbers.

Q1551 We have a pattern of 34 dots arranged and may remove any three dots, provided that one of them is exactly midway between the other two; then to remove another three dots under the same condition; and so on.  If we remove 33 dots, which are the possibilities for the remaining dot?

Q1541 Consider $29x+30y+31z=366$ where $x,y,z$ are positive integers with $x<y<z$.
(a) Without writing or using a computer, find such $x,y,z$.
(b) Prove that there is only one solution.