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National and Regional Contests
PEN Problems
PEN E Problems
29
29
Part of
PEN E Problems
Problems
(1)
E 29
Source:
5/25/2007
Let
s
n
s_n
s
n
denote the sum of the first
n
n
n
primes. Prove that for each
n
n
n
there exists an integer whose square lies between
s
n
s_n
s
n
and
s
n
+
1
s_{n+1}
s
n
+
1
.