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North Korea Team Selection Test
2013 North Korea Team Selection Test
3
3
Part of
2013 North Korea Team Selection Test
Problems
(1)
a^n + 2^n divides b^n + c
Source: North Korea Team Selection Test 2013 #3
5/17/2014
Find all
a
,
b
,
c
∈
Z
a, b, c \in \mathbb{Z}
a
,
b
,
c
∈
Z
,
c
≥
0
c \ge 0
c
≥
0
such that
a
n
+
2
n
∣
b
n
+
c
a^n + 2^n | b^n + c
a
n
+
2
n
∣
b
n
+
c
for all positive integers
n
n
n
where
2
a
b
2ab
2
ab
is non-square.
modular arithmetic
quadratics
number theory
North Korea
TST
Divisibility