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2010 Ukraine Team Selection Test
6
6
Part of
2010 Ukraine Team Selection Test
Problems
(1)
(c^n+1)/(2^na+b) is an integer for all n
Source: Ukraine TST 2010 p6
5/4/2020
Find all pairs of odd integers
a
a
a
and
b
b
b
for which there exists a natural number
c
c
c
such that the number
c
n
+
1
2
n
a
+
b
\frac{c^n+1}{2^na+b}
2
n
a
+
b
c
n
+
1
is integer for all natural
n
n
n
.
number theory
Integer
Divisibility