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Putnam
1940 Putnam
A1
A1
Part of
1940 Putnam
Problems
(1)
Putnam 1940 A1
Source: Putnam 1940
2/22/2022
Prove that if
f
(
x
)
f(x)
f
(
x
)
is a polynomial with integer coefficients and there exists an integer
k
k
k
such that none of
f
(
1
)
,
…
,
f
(
k
)
f(1),\ldots,f(k)
f
(
1
)
,
…
,
f
(
k
)
is divisible by
k
k
k
, then
f
(
x
)
f(x)
f
(
x
)
has no integral root.
Putnam
algebra
polynomial
calculus
integration