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3
(2^{4n+2}+1)/65 (i) integer, (ii) prime
(2^{4n+2}+1)/65 (i) integer, (ii) prime
Source: JBMO 2016 Shortlist N3
October 14, 2017
JBMO
number theory
Problem Statement
Find all positive integers
n
n
n
such that the number
A
n
=
2
4
n
+
2
+
1
65
A_n =\frac{ 2^{4n+2}+1}{65}
A
n
=
65
2
4
n
+
2
+
1
is a) an integer, b) a prime.
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