There has been much said in the popular media about declining standards and participation in secondary school mathematics in Australia.
It is strange that it should be so, but it is true all the same, that many of the most debated aspects of Mathematics concern matters that are really completely trivial.
The problem of how to successfully choose the partner most likely to lead to a long and happy marriage is a task which has occupied the minds of young and older people alike, men and women, among all races and cultures, throughout the ages.
A Pythagorean triad $(x,y,u)$ consists of positive integers $x,y,u$ such that $x^2+y^2=u^2$. Geometrically, the integers represent the lengths of the sides of a right-angled-triangle with the hypotenuse $u$.
Junior Division - Problems and Solutions
Competition Winners – Senior Division
First Prize
Sampson Wong James Ruse Agricultural High School
Q1301 (Suggested by J.Guest, Victoria) Solve the quartic $(x+1)(x+5)(x-3)(x-7) = -135.$
Q1302 Let $\alpha$, $\beta$ and $\gamma$ be the angles of one triangle.
Q1291 Show that there do not exist three primes $x$, $y$ and $z$ satisfying $$x^2 + y^3 = z^4$$
ANS: (Correct solution by J.C.