MathDB

3

Part of 2016 JBMO Shortlist

Problems(2)

Find all the pairs of integers $ (m, n)$

Source: JBMO 2016 shortlist , A3

6/25/2017
Find all the pairs of integers (m,n) (m, n) such that n+2016+m−2016∈Q. \sqrt {n +\sqrt {2016}} +\sqrt {m-\sqrt {2016}} \in \mathbb {Q}.
algebranumber theory
(2^{4n+2}+1)/65 (i) integer, (ii) prime

Source: JBMO 2016 Shortlist N3

10/14/2017
Find all positive integers nn such that the number An=24n+2+165A_n =\frac{ 2^{4n+2}+1}{65} is a) an integer, b) a prime.
JBMOnumber theory