1977 Canadian MO Problems

From AoPSWiki

The seven problems were all on the same day.

Problem 1

If prove that the equation has no solutions in positive integers and

Solution

Problem 2

Let be the center of a circle and be a fixed interior point of the circle different from Determine all points on the circumference of the circle such that the angle is a maximum.

Solution

Problem 3

is an integer whose representation in base is Find the smallest positive integer for which is the fourth power of an integer.

Solution

Problem 4

Solution

Problem 5

Solution

Problem 6

Solution

Problem 7

Solution

Resources

• 1977 Canadian MO
• Canadian Mathematical Olympiad
• Canadian MO Problems and Solutions