MathDB
Problems
Contests
National and Regional Contests
Saudi Arabia Contests
Saudi Arabia Pre-TST + Training Tests
2011 Saudi Arabia Pre-TST
3
\sqrt[n]{3^n+ 4^n+5^n+8^n+10^n} is an integer
\sqrt[n]{3^n+ 4^n+5^n+8^n+10^n} is an integer
Source: 2011 Saudi Arabia Pre-TST January p3
January 1, 2022
number theory
radical
Integer
Problem Statement
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.
Back to Problems
View on AoPS