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Azerbaijan Junior National Olympiad
2016 Azerbaijan Junior Mathematical Olympiad
2
2
Part of
2016 Azerbaijan Junior Mathematical Olympiad
Problems
(1)
Algebra.
Source:
2/7/2016
Prove that if for a real number
a
a
a
,
a
+
1
a
a+\frac {1}{a}
a
+
a
1
is integer then
a
n
+
1
a
n
a^n+\frac {1}{a^n}
a
n
+
a
n
1
is also integer where
n
n
n
is positive integer.
induction
algebra
number theory