Permanent problem IDPPL 073
Number theory
Let Y(x) be the maximal y such that there exists a choice of congruence classes a_p for all primes p≤ x such that every integer in [1,y] is congruent to at least one of the a_p\pmod{p}. Give good estimates for Y(x). In particular, can one prove that Y(x)=o(x^2) or even Y(x)≪ x^(1+o(1))?
Let Y(x) be the maximal y such that there exists a choice of congruence classes a_p for all primes p≤ x such that every integer in [1,y] is congruent to at least one of the a_p\pmod{p}. Give good estimates for Y(x). In particular, can one prove that Y(x)=o(x^2) or even Y(x)≪ x^(1+o(1))?
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