Applications of Modular Inverses

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Cierra Henderson, MBA |
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Cierra is an educational consultant and curriculum developer who has worked with students in K-12 for a variety of subjects including English and Math as well as test prep. She specializes in one-on-one support for students especially those with learning differences. She holds an MBA from the University of Massachusetts Amherst and a certificate in educational consulting from UC Irvine.
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| Questions: 10 | Updated: Dec 9, 2025
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1) Solve 3x ≡ 1 (mod 7).

Explanation

Inverse of 3 mod 7 is 5 → x = 5.

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About This Quiz
Applications Of Modular Inverses - Quiz

From solving congruences to cryptography, modular inverses are powerful tools! In this quiz, you’ll apply inverses to solve modular equations and connect them to real-world uses like secure communication. Try this quiz to practice solving with inverses and understand why they’re so important in mathematics and beyond.

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2) Solve 4x ≡ 1 (mod 9).

Explanation

4 × 7 = 28; 28 mod 9 = 1 → x = 7.

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3) Solve 7x ≡ 1 (mod 11).

Explanation

7 × 8 = 56; 56 mod 11 = 1 → x = 8.

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4) Solve 5x ≡ 1 (mod 12).

Explanation

5 × 5 = 25; 25 mod 12 = 1 → x = 5.

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5) Solve 2x ≡ 1 (mod 13).

Explanation

2 × 7 = 14; 14 mod 13 = 1 → x = 7.

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6) Solve 9x ≡ 1 (mod 14).

Explanation

9 × 11 = 99; 99 mod 14 = 1 → x = 11.

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7) Solve 11x ≡ 1 (mod 20).

Explanation

11 × 11 = 121; 121 mod 20 = 1 → x = 11.

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8) Solve 8x ≡ 1 (mod 15).

Explanation

8 × 2 = 16; 16 mod 15 = 1 → x = 2.

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9) Solve 6x ≡ 1 (mod 17).

Explanation

6 × 3 = 18; 18 mod 17 = 1 → x = 3.

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10) A cryptography system requires finding the inverse of 7 mod 26. What is it?

Explanation

7 × 15 = 105; 105 mod 26 = 1 → inverse is 15.

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Cierra Henderson |MBA |
K-12 Expert
Cierra is an educational consultant and curriculum developer who has worked with students in K-12 for a variety of subjects including English and Math as well as test prep. She specializes in one-on-one support for students especially those with learning differences. She holds an MBA from the University of Massachusetts Amherst and a certificate in educational consulting from UC Irvine.
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Solve 3x ≡ 1 (mod 7).
Solve 4x ≡ 1 (mod 9).
Solve 7x ≡ 1 (mod 11).
Solve 5x ≡ 1 (mod 12).
Solve 2x ≡ 1 (mod 13).
Solve 9x ≡ 1 (mod 14).
Solve 11x ≡ 1 (mod 20).
Solve 8x ≡ 1 (mod 15).
Solve 6x ≡ 1 (mod 17).
A cryptography system requires finding the inverse of 7 mod 26. What...
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