Properties of Modular Inverses

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1) If a × b ≡ 1 (mod n), then b is:

Explanation

By definition, b is the modular inverse of a mod n.

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About This Quiz
Properties Of Modular Inverses - Quiz

Modular inverses follow fascinating rules based on number properties. In this quiz, you’ll discover the conditions for an inverse to exist, how greatest common divisors (GCDs) play a role, and why every nonzero number has an inverse modulo a prime. We bring you this quiz to help you see the... see morestructure behind modular systems. see less

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2) Which number has no modular inverse mod 12?

Explanation

gcd(6,12) = 6 ≠ 1 → no inverse.

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3) If 3 × x ≡ 1 (mod 13), what is x?

Explanation

3 × 9 = 27; 27 mod 13 = 1. So x = 9.

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4) Which statement about modular inverses is true?

Explanation

A number has a modular inverse with respect to n if it is relatively prime to n, meaning their greatest common divisor (gcd) is 1. Therefore, option C is the correct statement regarding modular inverses.

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5) Find the modular inverse of 7 mod 26.

Explanation

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

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6) If 9 × x ≡ 1 (mod 23), what is x?

Explanation

9 × 18 = 162; 162 mod 23 = 1. So x = 18.

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7) Which of these numbers has an inverse mod 21?

Explanation

gcd(10,21) = 1 → 10 has an inverse.

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8) Which number is the modular inverse of 4 mod 17?

Explanation

4 × 13 = 52; 52 mod 17 = 1. So the inverse is 13.

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9) If 5 × y ≡ 1 (mod 19), what is y?

Explanation

5 × 4 = 20; 20 mod 19 = 1. So y = 4.

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10) Which of these is true about inverses mod a prime number p?

Explanation

In modular arithmetic, particularly with a prime modulus p, every nonzero integer less than p has a unique multiplicative inverse. This is because a prime number has no divisors other than 1 and itself, ensuring that the equation ax ≡ 1 (mod p) has a solution for every a in the range 1 to p-1.

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If a × b ≡ 1 (mod n), then b is:
Which number has no modular inverse mod 12?
If 3 × x ≡ 1 (mod 13), what is x?
Which statement about modular inverses is true?
Find the modular inverse of 7 mod 26.
If 9 × x ≡ 1 (mod 23), what is x?
Which of these numbers has an inverse mod 21?
Which number is the modular inverse of 4 mod 17?
If 5 × y ≡ 1 (mod 19), what is y?
Which of these is true about inverses mod a prime number p?
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