Volume 4


A theorem of twentieth century mathematics which must surely earn a place in any list of the great theorems of mathematics, is the theorem of Kurt Gödel concerning the existence of undecidable statements in formalised arithmetic.

J101 In $n$ is a positive integer other than $2,3$ or $5$, any square can be dissected into $n$ smaller squares.

J91 (i) Find all whole numbers such that when the third digit is deleted, the resulting number divides the original one.

If $a,b,c$, are any three numbers show that
$$a^2 + b^2 + c^2 \geq ab + bc + ca $$