# 1975 Canadian MO Problems

## Contents

## Problem 1

Simplify .

## Problem 2

A sequence of numbers satisfies

Determine the value of

## Problem 3

For each real number , denotes the largest integer less than or equal to , Indicate on the -plane the set of all points for which .

## Problem 4

For a positive number such as , is referred to as the integral part of the number and as the decimal part. Find a positive number such that its decimal part, its integral part, and the number itself form a geometric progression.

## Problem 5

are four "consecutive" points on the circumference of a circle and are points on the circumference which are respectively the midpoints of the arcs Prove that is perpendicular to .

## Problem 6

## Problem 7

A function is if there is a positive integer such that for all . For example, is periodic with period . Is the function periodic? Prove your assertion.

## Problem 8

Let be a positive integer. Find all polynomials where the are real, which satisfy the equation .