Inverse Modulo Calculator

How to Use the Inverse Modulo Calculator

Step 1: Enter the Inputs

Begin by locating the input fields labeled Number (a) and Modulus (m).

• Number (a): Enter an integer value for the number ‘a’. Ensure that this value is at least 1, as values less than 1 are not valid.
• Modulus (m): Enter an integer value for the modulus ‘m’. Ensure that this value is at least 2, as modulus values below 2 are not valid.

Step 2: Understanding the Result Fields

Once the values are entered, review the following result fields to understand the calculations and results:

• GCD(a, m): This field displays the greatest common divisor (GCD) of the number ‘a’ and the modulus ‘m’. The GCD is a critical value in determining if an inverse exists.
• Inverse Exists: This field reveals whether the modular inverse of ‘a’ with respect to modulus ‘m’ exists. If the GCD is 1, the inverse will exist, and “Yes” will be displayed. Otherwise, the display will show “No”.
• Modular Inverse: If an inverse exists, this field will provide the calculated modular inverse of ‘a’ under modulus ‘m’. If the inverse does not exist, it will state “Does not exist”.
• Verification (a⁻¹ × a ≡ 1 mod m): This field offers a verification of the modular inverse calculation. It multiplies the calculated inverse by ‘a’ and checks if the result is congruent to 1 modulo ‘m’. If no inverse exists, this will display “N/A”.

Step 3: Analyze the Results

After reviewing the results, analyze if the modular inverse calculation aligns with your expectations. The results provide not only the modular inverse but also assurance through verification of the calculation.

Conclusion

The Inverse Modulo Calculator is a valuable tool for determining modular inverses and ensuring accuracy via GCD and verification processes. Follow these steps to effectively utilize the calculator and understand all intermediate calculations.