Volume 45
, Issue 1

2009

Welcome to this  first issue for 2009. The first article in this issue is a peer reviewed (Section A) article by Christian Aebi and Grant Cairns.
Problem 461 from Parabola (Volume 16, Issue 2, p.32) asked: Partition the set $P_n=\{2,3,5,\dots,p_n\}$ of the first $n$ primes into two nonempty disjoint parts $A,B$ and let $a, b$  be their respective products.

As a broad generalisation we might say that research in mathematics consists of two parts: finding out what is true, and proving that it is true.

A 2007 book tells a very interesting story.
It is called The Archimedes Codex and it recounts how a lost work by that great Greek mathematician recently came to light.  The authors are Reviel Netz, a mathematical historian, and William Noel, the curator of the museum that holds it.

Q1291 Show that there do not exist three primes $x$, $y$ and $z$ satisfying $$x^2 + y^3 = z^4$$.

Q1281 Prove that for any real numbers $a$ and $b$ there holds  $\frac{1+|a|}{1+|b|} \leq 1 + |a-b|.$