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Romanian Masters of Mathematics Collection
2012 Romanian Master of Mathematics
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2012 Romanian Master of Mathematics
Problems
(1)
Infinitely many positive integers n
Source: Romanian Master Of Mathematics 2012
3/3/2012
Prove that there are infinitely many positive integers
n
n
n
such that
2
2
n
+
1
+
1
2^{2^n+1}+1
2
2
n
+
1
+
1
is divisible by
n
n
n
but
2
n
+
1
2^n+1
2
n
+
1
is not.(Russia) Valery Senderov
modular arithmetic
function
number theory
number theory proposed