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1971 IMO Longlists
44
44
Part of
1971 IMO Longlists
Problems
(1)
Let's use nu (n) instead of pi (n)! [ILL 1971]
Source:
1/1/2011
Let
m
m
m
and
n
n
n
denote integers greater than
1
1
1
, and let
ν
(
n
)
\nu (n)
ν
(
n
)
be the number of primes less than or equal to
n
n
n
. Show that if the equation
n
ν
(
n
)
=
m
\frac{n}{\nu(n)}=m
ν
(
n
)
n
=
m
has a solution, then so does the equation
n
ν
(
n
)
=
m
−
1
\frac{n}{\nu(n)}=m-1
ν
(
n
)
n
=
m
−
1
.
induction
logarithms
number theory proposed
number theory