1975 Canadian MO Problems
Contents
[hide]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
.