Year 1993 - Volume 29
2020 - Present

Peter Brown
You have (hopefully) learnt a little bit at school about geometric series, and have studied so-called 'limiting sums' of geometric series.

George Harvey
Under what conditions is an increment of $b paid k times a year [Option(B)] more advantageous than an annual increment of$a paid yearly [Option (A)]?

Rod James
In the last issue of Parabola, the question was posed as to whether it is better to work for Company A (with an annual rise of $2,000 or Company B (with only a six-monthly rise of$500 ).

Alex Opie
When overseas economists tackle the problem of supply and demand they like to talk about pig-iron, hogs and corn.

Esther Szekeres has provided us with a non-trigonometrical solution to Question 866.

Q.882 A triangle is divided by one straight line into two parts which are similar to each other. Prove that the triangle is isosceles or right-angled (or both).

Q.872 A flea on the number line jumps from the point a to the point b , given by a+(1/b)=1 .

John Steele
Common sense tells us that either two things happen at the same time or they do not.

George Szekeres
In a previous issue of Parabola (Vol 28 No 1, p26) David Tacon has written about prime numbers, that is integers greater than one which have only 1 and themselves as divisors.

Junior Division
1. Given real numbers a,b with 0a ≤ b, a
sequence of numbers is defined by

x1 = a, x2 = b,xn+2 = |xn+1| - xn for ≥1

Q.893 Find all positive integer solutions of x2−84=6y+3x−2xy

Q.882 A triangle is divided by one straight line into two parts which are similar to each other. Prove that the triangle is isosceles or right-angled (or both).

In the last issue of Parabola George Szekeres (see the end of his article on Carmichael numbers) stated that one of the most famous problems in mathematics, Fermat's last theorem, appeared to have been solved.

Peter Brown
In my first year at university, our lecturer offered a \$100 prize to anyone who could work out ∫e−x2dx

James Franklin
Proof is what makes mathematics different from other sciences.

John Dixon
Before reading the rest of this article try to prove the following statements.
1. If a drawer contains a large number of socks of the same colour but two different sizes, and I take out three socks, then two of these will make a pair.

David Tacon
Consider a fixed reflector R on the rim of a bicycle wheel of radius r .

One of the questions common to the Senior and Junior divisions of this year's School Mathematics Competition was the following.

Q.903 Find all positive integers n such that 1+2+3+⋯+n is a factor of 1×2×3×⋯×n .

Q.893 Find all positive integer solutions of
x2−84=6y+3x−2xy.