Given $a,b$ positive numbers such that $gcd(a,b)=1$.Prove that there are infinitely many $n$ positive integers such that $x_n=a+nb$ sequence has many terms such that it is not divisible by any prime's square.
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$\begingroup$ Maybe you can reformulate it more properly ? $\endgroup$– G. MelfiCommented Aug 24 at 16:24
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Dirichlet's theorem ensures that $x_n$ contains infinitely many primes, so in particular infinitely many terms that are not divisible by any prime's squares.
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$\begingroup$ Thanks for saying this theorem,I searched everywhere on internet but could not find the solution with enumeration.If you have,can you please share? $\endgroup$ Commented Aug 24 at 17:44
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2$\begingroup$ This question is obviously not research level so I don't think you should answer it; better to just leave a comment. $\endgroup$ Commented Aug 24 at 19:44
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$\begingroup$ I agree with you that the question is not of research level. However my sentence is an answer, and at the same time it shows why the question is not of research level. $\endgroup$– G. MelfiCommented Aug 25 at 7:30
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1$\begingroup$ @G.Melfi which is exactly why it would be better as a comment... $\endgroup$ Commented Aug 25 at 12:39