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National and Regional Contests
Mexico Contests
Regional Olympiad of Mexico Center Zone
2015 Regional Olympiad of Mexico Center Zone
4
4
Part of
2015 Regional Olympiad of Mexico Center Zone
Problems
(1)
prime condition
Source: Mexico Regional Olympiad
9/26/2015
Find all natural integers
m
,
n
m, n
m
,
n
such that
m
,
2
+
m
,
2
n
+
m
,
2
+
2
n
+
m
m, 2+m, 2^n+m, 2+2^n+m
m
,
2
+
m
,
2
n
+
m
,
2
+
2
n
+
m
are all prime numbers
number theory