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Number theory
Date added
Erdős problem 978 - part ii
If k>3 (and k=2l), and for all primes p
there exists
n
such that
pk−2∤f(n)
,
then are there infinitely many
n
for which
f(n)
is
(k−2)
-power-free?
$1,401 bounty·nobody has started
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Solve it
Nobody has attempted this. A complete proof or refutation takes the whole bounty.
[Ho67] Hooley, C., On the power free values of polynomials. Mathematika (1967), 21--26.
[Br11] Browning, T. D., Power-free values of polynomials. Arch. Math. (Basel) (2011), 139--150.
[Er53] Erdős, P., Arithmetical properties of polynomials. J. London Math. Soc. (1953), 416--425.
Something wrong with this formalization?
A statement that does not faithfully capture the original conjecture is the one real risk here, so we would rather hear about it early - before someone spends weeks on it.
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