LaTeX
\varphi(n)=n\prod_{p\mid n}\left(1-\frac1p\right)Variables
- Define all variables, domains, and units before substitution.
How to use this formula
Computes Euler totient from the distinct prime divisors of n.
Important notes
- Verify assumptions and conventions before use.
Quick example
Apply the euler totient product to a small known case and verify the result.
Applicability, worked calculation, and verification
Assumptions and domain checks
- Verify assumptions and conventions before use.
- For the Euler Totient Product, every denominator must be nonzero, and the numerator and denominator must remain correctly grouped.
- For the Euler Totient Product, 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 euler totient product to a small known case and verify the result.
Common mistakes
- When copying Euler Totient Product, keep the complete numerator and denominator grouped; a missing brace or parenthesis changes the result.
- Verify the result of Euler Totient Product with a known case, inverse operation, dimensional check, or independent calculation before publishing it.
Continue the workflow
Use Euler Totient Product 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
\varphi(n)=n\prod_{p\mid n}\left(1-\frac1p\right). - 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 Euler Totient Product used for?
Computes Euler totient from the distinct prime divisors of n.
Can I copy this formula as LaTeX?
Yes. Copy \varphi(n)=n\prod_{p\mid n}\left(1-\frac1p\right) 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.