Garner's Algorithm — Mixed-Radix CRT Reconstruction

Rebuild x from residues x mod pᵢ. Solve each mixed-radix digit aᵢ in turn (subtract the partial, multiply by the prefix-product inverse mod pᵢ) and accumulate x = a₀ + a₁p₀ + a₂p₀p₁ + …

step 0

Inputs & current digit solve

Each digit aᵢ is solved mod pᵢ only — no giant products.
column being solved digit solved

Mixed-radix digits & running value

running reconstructed value x =
0
Press Step to begin. We reconstruct x digit by digit using Garner's mixed-radix method.
Self-contained visualization. Garner reconstruction over pairwise-coprime moduli. The digit solve uses only arithmetic mod a single prime pᵢ; the running value x = Σ aᵢ·Wᵢ (with prefix products Wᵢ = p₀·…·pᵢ₋₁) accumulates as digits appear. See junior.md and professional.md for the uniqueness and correctness proofs.