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(c^n+1)/(2^na+b) is an integer for all n

Source: Ukraine TST 2010 p6

May 4, 2020

number theoryIntegerDivisibility

Problem Statement

Find all pairs of odd integers

a

and

b

for which there exists a natural number

c

such that the number

\frac{c^n+1}{2^na+b}

is integer for all natural

n

.

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