Volume 7
, Issue 1

1971

It has been said that "behind every great computer there is a great memory". As with most sayings, of course, this is not the whole story.

As will be known, when we write $12 \equiv 7 \text{(modulo) } 5$ we are expressing the fact that both $12$ and $7$ have the same remainder when divided by $5$.

J141 The real numbers $a,b$ and $c$ are such that $$a^2 + 4b^2 + 9c^2 = 2ab + 6bc + 3ca.$$ Prove that $$a = 2b = 3c.$$

Solve for $x,y$ and $z$ the simultaneous system of equations
\begin{align*}
x(x+y) + z(x-y) & = a, \\
y(y+z) + x(y-z) & = b, \\
z(z+x) + y(z-x) & = c,
\end{align*}

J131 (i) How many lines equidistant from three given points can be drawn in the plane?