Because the prime factor set (NP _ α = {p _ α ∈ p _ α: 2 [≤ p] _ α, √n→∞}) is a known set, all the composite numbers belong to only one of its smallest prime factor family sets (nd _ (σ≤ α) d _ α). Decomposition of prime factors of integers with division, solution of (n 2) and high-order (n s) indefinite equations, determination of solvability of Legendre symbols (a/p_i) and Jacobian symbols (n/m) to equations, and Euler function, etc.<br> Are simplified or omitted together. The family screening method () is carried out in the order of prime factors from small to large, and any composite number that overlaps with the current prime factor is naturally filtered, which reshapes the prime factor and composite number into a simple and clear subordinate relationship, greatly simplifying the solution of composite number set.
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