LaTeX
x\equiv\sum_i a_iM_iN_i\pmod MVariables
- Define all variables, domains, and units before substitution.
How to use this formula
Reconstructs a simultaneous congruence solution under coprime moduli.
Important notes
- Verify assumptions and conventions before use.
Quick example
Apply the chinese remainder reconstruction to a small known case and verify the result.
Applicability, worked calculation, and verification
Assumptions and domain checks
- Verify assumptions and conventions before use.
- The plus-minus sign represents separate branches; evaluate and verify both when both are admissible.
- For the Chinese Remainder Reconstruction, the index variable, lower bound, upper bound, and any empty-sum or empty-product convention must be clear.
- Apply the formula over the intended integer domain and check divisibility, coprimality, parity, or modulus conditions.
Worked example
Apply the chinese remainder reconstruction to a small known case and verify the result.
Common mistakes
- Do not collapse the ± in Chinese Remainder Reconstruction into one value; calculate each admissible branch and check it in the original problem.
- Verify the result of Chinese Remainder Reconstruction with a known case, inverse operation, dimensional check, or independent calculation before publishing it.
Continue the workflow
Use Chinese Remainder Reconstruction in your own work
- Check the domainMatch the variables and assumptions to the problem before substituting values.
- Copy the exact notationPreserve grouping, signs, and exponents in
x\equiv\sum_i a_iM_iN_i\pmod M. - Edit or convertOpen the expression in the LaTeX editor, then export it for your document or web page.
Review and verification
Last reviewed: 2026-07-23
Automated quality check: Kept noindex until the missing evidence is supplied.
Formula references
- Digital Library of Mathematical FunctionsNational Institute of Standards and Technology — Definitions, notation, identities, and reference material for mathematical functions.
Frequently asked questions
What is the Chinese Remainder Reconstruction used for?
Reconstructs a simultaneous congruence solution under coprime moduli.
Can I copy this formula as LaTeX?
Yes. Copy x\equiv\sum_i a_iM_iN_i\pmod M or open it in the LaTeX editor.
What should I check before using it?
Confirm that each variable, unit, domain restriction, and assumption matches the problem.