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National and Regional Contests
Vietnam Contests
Vietnam Team Selection Test
1998 Vietnam Team Selection Test
3
sum of primes fractions > ln(ln(m))
sum of primes fractions > ln(ln(m))
Source: Vietnam TST 1998 for the 39th IMO, problem 3
June 26, 2005
algebra unsolved
algebra
Problem Statement
Let
p
(
1
)
,
p
(
2
)
,
…
,
p
(
k
)
p(1), p(2), \ldots, p(k)
p
(
1
)
,
p
(
2
)
,
…
,
p
(
k
)
be all primes smaller than
m
m
m
, prove that
∑
i
=
1
k
1
p
(
i
)
+
1
p
(
i
)
2
>
l
n
(
l
n
(
m
)
)
.
\sum^{k}_{i=1} \frac{1}{p(i)} + \frac{1}{p(i)^2} > ln(ln(m)).
i
=
1
∑
k
p
(
i
)
1
+
p
(
i
)
2
1
>
l
n
(
l
n
(
m
))
.
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