Inverse Modulo Calculator

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Inverse Modulo

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What is Inverse Modulo?

A modular inverse is a value that undoes addition or multiplication under a modulus.

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How to Use This Calculator

  1. Enter or select Inverse type, a, Modulus m.
  2. Check the unit beside each measurement. For a percentage or rate, use the scale and time period stated in the form.
  3. Choose Calculate, then compare the output with the formula and example below. If you change a value or option, calculate again to update the result.
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Formula Used

Additive: (a + x) mod m = 0; multiplicative: ax mod m = 1
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Variables Explained

InputWhat it means
Inverse typeChoose the applicable option; it determines which relationship or conversion the page applies.
aA value or coefficient in the formula above; keep the displayed position and sign.
Modulus mUse the measured or stated value for this item, with the unit or category shown beside the field.
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Worked Example

Modulo 7, the additive inverse of 3 is 4 and its multiplicative inverse is 5.

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Why Use This Calculator?

Solve modular equations where ordinary division is unavailable.

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Common Mistakes

    • A multiplicative inverse exists only when a and m are coprime.
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Frequently Asked Questions

Should I round numbers before calculating?

Keep the original input precision through the calculation and round the final answer to the precision you need. Rounding an intermediate result can change later steps.

Why can a manual calculation differ slightly?

Check the operation, units, signs and rounding first. Equivalent fractions or expressions can look different while representing the same value.

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Sources & References