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Putnam
1956 Putnam
B7
B7
Part of
1956 Putnam
Problems
(1)
Putnam 1956 B7
Source: Putnam 1956
7/5/2022
The polynomials
P
(
z
)
P(z)
P
(
z
)
and
Q
(
z
)
Q(z)
Q
(
z
)
with complex coefficients have the same set of numbers for their zeros but possibly different multiplicities. The same is true for the polynomials
P
(
z
)
+
1
and
Q
(
z
)
+
1.
P(z)+1 \;\; \text{and} \;\; Q(z)+1.
P
(
z
)
+
1
and
Q
(
z
)
+
1.
Prove that
P
(
z
)
=
Q
(
z
)
.
P(z)=Q(z).
P
(
z
)
=
Q
(
z
)
.
Putnam
algebra
polynomial
roots