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Tuesday, September 16, 2008

Q) 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:

sumit said...

very good friend