Regular readers know of my affinity for number theory. Today’s exercise is a reflection of that.

It is conjectured that the two numbers produced by the equations n17 + 9 and (n + 1)17 + 9 for a given n are always co-prime (that is, their greatest common divisor is 1). Is that conjecture correct?

Your task is to either prove that the greatest common divisor is always 1 or write a program that finds a case where the greatest common divisor is not 1. When you are finished, you are welcome to read or run a suggested solution, or to post your own solution or discuss the exercise in the comments below.

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