MathDB

For the positive integers

a, b, x_1

we construct the sequence of numbers

(x_n)_{n=1}^{\infty}

such that

x_n = ax_{n-1} + b

for each

n \ge 2

. Specify the conditions for the given numbers

a, b

and

x_1

which are necessary and sufficient for all indexes

m, n

to apply the implication

m | n \Rightarrow x_m | x_n

.
(Jaromír Šimša)

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