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Prime numbers, diophantine equations, diophantine approximations, analytic or algebraic number theory, arithmetic geometry, Galois theory, transcendental number theory, continued fractions

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Enumerative number theory term searching [closed]

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 …
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