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Putnam
2010 Putnam
B4
B4
Part of
2010 Putnam
Problems
(1)
Putnam 2010 B4
Source:
12/6/2010
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.
Putnam
algebra
polynomial
function
induction
rational function
recursion