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Tournament Of Towns
1982 Tournament Of Towns
(027) 1
(027) 1
Part of
1982 Tournament Of Towns
Problems
(1)
TOT 027 1982 Autumn S1 sum [ \sqrt[i]{n}] = sum [\log_i n]
Source:
8/18/2019
Prove that for all natural numbers
n
n
n
greater than
1
1
1
:
[
n
]
+
[
n
3
]
+
.
.
.
+
[
n
n
]
=
[
log
2
n
]
+
[
log
3
n
]
+
.
.
.
+
[
log
n
n
]
[\sqrt{n}] + [\sqrt[3]{n}] +...+[ \sqrt[n]{n}] = [\log_2 n] + [\log_3 n] + ... + [\log_n n]
[
n
]
+
[
3
n
]
+
...
+
[
n
n
]
=
[
lo
g
2
n
]
+
[
lo
g
3
n
]
+
...
+
[
lo
g
n
n
]
(VV Kisil)
floor function
radical
logarithm
Sum
algebra