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Erdős problem 202

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Let n1<⋯<nr≤Nn_1<\cdots < n_r\leq N with associated ai(modni)a_i\pmod{n_i} such that the congruence classes are disjoint (that is, every integer is ≡ai(modni)\equiv a_i\pmod{n_i} for at most one 1≤i≤r1\leq i\leq r). How large can rr be in terms of NN?

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