Difference between revisions of "1971 Canadian MO Problems"
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Show that, for all integers <math>n</math>, <math>n^2+2n+12</math> is not a multiple of 121. | Show that, for all integers <math>n</math>, <math>n^2+2n+12</math> is not a multiple of 121. | ||
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[[1971 Canadian MO Problems/Problem 6 | Solution]] | [[1971 Canadian MO Problems/Problem 6 | Solution]] | ||
Revision as of 21:49, 13 December 2011
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Contents
[hide]Problem 1
is a chord of a circle such that
and
Let
be the center of the circle. Join
and extend
to cut the circle at
Given
find the radius of the circle
Problem 2
Let and
be positive real numbers such that
. Show that
.
Problem 3
is a quadrilateral with
. If
is greater than
, prove that
.
Problem 4
Determine all real numbers such that the two polynomials
and
have at least one root in common.
Problem 5
Let , where the coefficients
are integers. If
and
are both odd, show that
has no integral roots.
Problem 6
Show that, for all integers ,
is not a multiple of 121.