**Consider a sequence { } such that**.

**How many distinct pairs chosen from this sequence have g.c.d.= 6 ?**

A) a1 = 2

a2 = 3

a3 = 7

a4 = 43

Now since

a(n+1) = a.n^2 - an + 1

and after a1, the next terms are odd...

so terms will be of the type

odd^2 - odd + 1

odd^2 is always odd... and odd^2 + 1 will become even.

then even - odd = odd always....

So there won't be any distinct pair with GCD = 6... 2 will be the only even number in the sequence.

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## 1 comment:

very good friend

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