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Saudi Arabia Contests
Saudi Arabia Pre-TST + Training Tests
2011 Saudi Arabia Pre-TST
3
3
Part of
2011 Saudi Arabia Pre-TST
Problems
(1)
\sqrt[n]{3^n+ 4^n+5^n+8^n+10^n} is an integer
Source: 2011 Saudi Arabia Pre-TST January p3
1/1/2022
Find all integers
n
≥
2
n \ge 2
n
≥
2
for which
3
n
+
4
n
+
5
n
+
8
n
+
1
0
n
n
\sqrt[n]{3^n+ 4^n+5^n+8^n+10^n}
n
3
n
+
4
n
+
5
n
+
8
n
+
1
0
n
is an integer.
number theory
radical
Integer