# Category Archives: Number theory, combinatorics

# STEP I-2006-1 and mental arithmetic

STEP I/2006/1 – Find the integer, n, that satisfies . Find also a small integer m such that is a perfect square. Hence express 33,127 in the form pq, where p and q are integers greater than 1.

By considering the possible factorisations of 33,127, show that there are exactly two values of m for which is a perfect square, and find the other value.