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Ask iit jee aieee pet cbse icse state board community Discussion Response Post to: Easy challenge in Number Theory - From Feynmann
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spideyunlimited (4185)

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Olaaa!! Perrrfect answer. 699  [1044 rates]

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a1 = 2. a2 = 3, a3 = 7, a4 = 43

Now since
a(n+1) = an^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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- Gaurav Ragtah (spideyunlimited)
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