Question

What is the maximum possible value of the greatest common divisor of two consecutive terms of the sequence $a_n = n! + n$, where $n \ge 0$?

Answer 1

2

Explanation:

You want the largest possible greatest common divisor of consecutive terms of the sequence an = n! +n.

Sequence

The sequence starts off 2, 4, 9, 28, 125, ...

The first two terms have a GCD of 2. The remaining pairs of terms have a GCD of 1.

The maximum possible GCD of adjacent terms is 2.

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