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Putnam
1967 Putnam
A3
A3
Part of
1967 Putnam
Problems
(1)
Putnam 1967 A3
Source: Putnam 1967
5/13/2022
Consider polynomial functions
a
x
2
ā
b
x
+
c
ax^2 -bx +c
a
x
2
ā
b
x
+
c
with integer coefficients which have two distinct zeros in the open interval
(
0
,
1
)
.
(0,1).
(
0
,
1
)
.
Exhibit with proof the least positive integer value of
a
a
a
for which such a polynomial exists.
Putnam
algebra
polynomial
function