1973 Canadian MO Problems
Contents
Problem 1
Solve the simultaneous inequalities,
and
; i.e. find a single inequality equivalent to the two simultaneous inequalities.
What is the greatest integer that satisfies both inequalities
and
.
Give a rational number between
and
.
Express
as a product of two integers neither of which is an integral multiple of
.
Without the use of logarithm tables evaluate
.
Problem 2
Problem 3
Problem 4
Problem 5
Problem 6
Problem 7
Observe that $\frac{1}{1}= \frac{1}{2}+\frac{1}{2};\quad \frac{1}{2}=\frac{1}{3}+\frac{1}{6};\quad \frac{1}{3}=\frac{1}{4}+\frac{1}{12};\qu...$ (Error compiling LaTeX. Unknown error_msg) State a general law suggested by these examples, and prove it.
Prove that for any integer greater than
there exist positive integers
and
such that