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

I'm not sure if it's 2 or not becuase there might be a higher answer...

 Aug 18, 2020
edited by ScaryMath  Aug 18, 2020
edited by ScaryMath  Aug 18, 2020
edited by ScaryMath  Aug 18, 2020
edited by ScaryMath  Aug 18, 2020
edited by ScaryMath  Aug 18, 2020
 #1
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2 should be the maximum. And that would occur when n =1 and n=2. 1!+1=2 and 2!+2 =4 and the GCD(2, 4)=2. Any two consecutive terms after 2 would have a GCD of 1. So: 3!+3 =9. 4!+4=28 and GCD(9, 28)=1...and so on.

 Aug 18, 2020

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