
#1
Oct907, 12:21 AM

P: 4

a question came up
"show that the arithmetic progression ax+b contains an infinite subsequence (not necessarily a progression), every two of whose elements are relatively prime." i have a hunch that the chinese remainder theorem has something to do with this, but I'm not sure how. any thoughts? 



#2
Oct907, 12:25 AM

P: 461

Is that true? What if a=2, b=o?




#3
Oct907, 12:30 AM

P: 4

sorry, assuming a, b are non zero




#4
Oct907, 12:50 AM

P: 461

arithmetic progressions
Then a=2, b=2 is a counterexample. I think you really need that a and b are coprime, in which case the sequence actually contains infinitely many primes.




#5
Oct907, 12:55 AM

P: 4

right again. its actually a two part question so it says on the top that (a,b) = 1, i forget to mention; if so (now that we finally got the problem) how is the CRT applicable here?




#6
Oct907, 01:13 AM

P: 4

and deriving some sort of solution that does not employ dirichlet's theorem, i think, because then that would be obvious; i really do not know how the CRT can be used here.



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