Modular Inverse Calculator evaluated example 1
Use the page’s labelled starter inputs to verify Modular Inverse Calculator.
Inputs- A: 3
- Modulus: 11
Evaluated result: 3⁻¹ ≡ 4 (mod 11)
Modular Inverse Calculator
Find the normalized multiplicative inverse of an integer modulo m when that inverse exists.
Modular Inverse Calculator
Result3⁻¹ ≡ 4 (mod 11)
What this calculator answers
Modular Inverse Calculator applies the registered method “use extended Euclid to return the normalized inverse of a modulo m exactly when gcd(a,m)=1” to the displayed A, Modulus inputs. Both worked examples come from the production calculation engine, and MIT OpenCourseWare — Mathematics for Computer Science defines the cited method or convention; no hidden inputs or current external data are inferred.
Variables, defaults, and limits
- A
- A is a structured text input. The displayed starter value is 3; it is an example, not a hidden assumption.
- Default: 3
- Accepted values: The field has no narrower HTML limit, but it must still satisfy the documented formula domain and produce a finite result.
- Modulus
- Modulus is a structured text input. The displayed starter value is 11; it is an example, not a hidden assumption.
- Default: 11
- Accepted values: The field has no narrower HTML limit, but it must still satisfy the documented formula domain and produce a finite result.
Formula and calculation rule
R=x₁⁻¹ mod x₂ iff gcd(x₁,x₂)=1; x₁=A; x₂=ModulusModular Inverse Calculator evaluates the registered expression “R=x₁⁻¹ mod x₂ iff gcd(x₁,x₂)=1; x₁=A; x₂=Modulus” with the validated inputs. Full calculation precision is retained until the result is formatted for display.
Worked examples
Modular Inverse Calculator evaluated example 2
Change one valid input or choice and evaluate Modular Inverse Calculator again to check that the result responds deterministically.
Inputs- A: 4
- Modulus: 11
Evaluated result: 4⁻¹ ≡ 3 (mod 11)
Assumptions
- Modular Inverse Calculator uses the visitor-entered values exactly as labelled; it does not retrieve private records or current rates.
- The calculation is limited to the declared relationship: R=x₁⁻¹ mod x₂ iff gcd(x₁,x₂)=1; x₁=A; x₂=Modulus.
- Intermediate values are not rounded; display rounding is applied only at the presentation boundary.
- The deterministic calculation runs locally and does not upload calculator inputs to the application API.
- The result is an educational arithmetic result and excludes facts that are not represented by an input.
Validation and boundaries
- Every visible required input must be present; a missing value is never replaced with zero.
- NaN, positive or negative infinity, unsafe overflow, and a non-finite final result are rejected.
- Field-specific minimums, maximums, and choices apply to A, Modulus.
- Zero, negative values, and discrete counts are accepted only when the displayed field definition permits them.
Review and correction links
Common mistakes
- Confirm the meaning and unit of A, Modulus before calculating; a numerically valid value can still use the wrong convention.
- Do not round intermediate values when checking the result, because early rounding can change the last displayed digits.
- Changing an unstated real-world assumption does not change the calculator until the corresponding displayed input is changed.
- Use the result as the answer to the displayed mathematical question, not to a different word problem with hidden conditions.
Frequently asked questions
- What question does Modular Inverse Calculator answer?
- Find the normalized multiplicative inverse of an integer modulo m when that inverse exists. The implemented relationship is R=x₁⁻¹ mod x₂ iff gcd(x₁,x₂)=1; x₁=A; x₂=Modulus.
- Which inputs does Modular Inverse Calculator use?
- It uses the visible fields A, Modulus. No hidden value is substituted for an omitted required input.
- What happens when Modular Inverse Calculator receives an invalid or extreme value?
- The page rejects missing, ambiguous, out-of-range, or non-finite values and refuses to display a non-finite result.
- Why can Modular Inverse Calculator differ from another result?
- Different unit conventions, endpoint policies, fee or rate assumptions, formula domains, and premature rounding can produce a different answer.
- Can I use Modular Inverse Calculator as professional advice?
- No. It answers the displayed mathematical question and cannot account for omitted real-world facts.
- How can I verify the Modular Inverse Calculator result?
- Recalculate the two evaluated examples without rounding intermediate values and compare the declared formula or convention with MIT OpenCourseWare — Mathematics for Computer Science.
Source and review scope
MIT OpenCourseWare — Mathematics for Computer Science
Scope: MIT OpenCourseWare — Mathematics for Computer Science is used to check the formula, definition, or convention relevant to Modular Inverse Calculator. The citation does not supply current personal, lender, tax, medical, or market data.
Source checked: