Volume 29
, Issue 2

1993

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

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 $0 < a \leq b$, a sequence of numbers is defined by $$x_1 = a, x_2 = b, x_{n+2} = \left|x_{n+1}\right| - x_n \text{ for } n \geq 1$$

Q.893 Find all positive integer solutions of $$x^2 - 84 = 6y + 3x - 2xy$$

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).