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Math Challenge for Enthusiasts

1) The document describes a math problem involving a cubic function f(x) = ax^3 + bx^2 + cx + d where a, b, c, and d are rational numbers. 2) It provides bounds for f(n) when n is an integer, except possibly when n = -2. 3) Readers are asked to (a) show that a = 1/3 and (b) find the value of f(102019) - f(102019 - 1).

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69 views1 page

Math Challenge for Enthusiasts

1) The document describes a math problem involving a cubic function f(x) = ax^3 + bx^2 + cx + d where a, b, c, and d are rational numbers. 2) It provides bounds for f(n) when n is an integer, except possibly when n = -2. 3) Readers are asked to (a) show that a = 1/3 and (b) find the value of f(102019) - f(102019 - 1).

Uploaded by

ElevenPlus Parents
Copyright
© © All Rights Reserved
We take content rights seriously. If you suspect this is your content, claim it here.
Available Formats
Download as PDF, TXT or read online on Scribd
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Problem of the Month

Problem 3: December 2019

Let a, b, c, and d be rational numbers and f (x) = ax3 + bx2 + cx + d. Suppose


f (n) is an integer whenever n is an integer and that
1 3 2 1 4
n − n − ≤ f (n) ≤ n3 + n2 + 2n +
3 3 3 3
for every integer n with the possible exception of n = −2.
1
(a) Show that a = .
3
(b) Find f (102019 ) − f (102019 − 1).

Webpage: cemc.uwaterloo.ca/resources/potm.php Email: potm@uwaterloo.ca

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