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#1 2007-09-22 22:34:10

tommy20
Guest

Sequence

We have sequence, wich is define by the conditions:



Decide if exist any integer number

and

#2 2019-05-19 02:39:03

Alg Num Theory
Member
Registered: 2017-11-24
Posts: 693
Website

Re: Sequence

It is clear that none of the terms in the sequence is divisible by 5. For

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Similarly none of the terms is divisible by 3, for

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It follows that

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i.e. consecutive terms are coprime; also

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i.e. alternate terms are coprime as well.

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Since a₁ = 1, k =1 fits the bill. And since the sequence is clearly strictly increasing, it is the only one that does.


Me, or the ugly man, whatever (3,3,6)

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