Advanced P12(BOMC 2)

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*Mahi*
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Advanced P12(BOMC 2)

Unread post by *Mahi* » Sun Apr 01, 2012 7:11 pm

Determine whether there exists a sequence of strictly increasing positive integers $\{ a_k \}^ \infty_{k=1}$ such that the sequence $\{a_k+x\}^\infty_{k=1}$ contains only finitely many primes for all integers $x$.
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*Mahi*
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Re: Advanced P12(BOMC 2)

Unread post by *Mahi* » Sun Apr 01, 2012 9:30 pm

Hint:
"Finitely many are prime" is'nt it a bit tough? Why don't we transform it to something easy like "in sequence $\{a_k\}^\infty_{k=0}$ finitely many are co-prime with "x"?
Desperate:
After some $i$, all of $a_i$'s are not co-prime with $x$.
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