Hash tree - learning

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Prime Resolution Theorem

M = P₁ * P₂ * P₃ * ... * P_n

For two numbers n ₁ , n _{2 in the interval [m, m+M]}

n ₁  Ξ n ₂ (mod P _i ) cannot always hold, 1 <= i <= n

The perceptual understanding is that n prime numbers can "resolve" an interval whose length is as long as their product.