Setup
Choose K primes p_i with ∏p_i > possible result. Each machine word.
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Per-prime computation
Run algorithm mod each p_i separately. All arithmetic in native ints. K× overhead.
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Reconstruction
CRT combines K residues into single big integer. Or into result if bound is known.
Applications
Big-integer polynomial multiplication. Determinant of integer matrix. Combinatorial identities where result may overflow.