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Putnam
2010 Putnam
B4
Putnam 2010 B4
Putnam 2010 B4
Source:
December 6, 2010
Putnam
algebra
polynomial
function
induction
rational function
recursion
Problem Statement
Find all pairs of polynomials
p
(
x
)
p(x)
p
(
x
)
and
q
(
x
)
q(x)
q
(
x
)
with real coefficients for which
p
(
x
)
q
(
x
+
1
)
ā
p
(
x
+
1
)
q
(
x
)
=
1.
p(x)q(x+1)-p(x+1)q(x)=1.
p
(
x
)
q
(
x
+
1
)
ā
p
(
x
+
1
)
q
(
x
)
=
1.
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