A multiplicative inverse of 3 modulo 5 is any integer a such that 3 a ≡ 1 (mod 5), hence for some a ∈ Z5.

Do such inverses exist for each element of Z5? If not, which ones?

Question

Computers and Technology

Frederick

3 March, 09:05

A multiplicative inverse of 3 modulo 5 is any integer a such that 3 a ≡ 1 (mod 5), hence for some a ∈ Z5.

Do such inverses exist for each element of Z5? If not, which ones?

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Answers (1)

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Yaka · Answer 1

The obvious element for which it can't exist is 0 as a*0=0 independent of modulo

all other elements have an inverse:

1*1≡1

2*3≡6≡1

3*2≡6≡1

4*4≡16≡1

if there are more than a few numbers/guessing is inefficient it can be calculated using the extended euclidean algorithm

A multiplicative inverse of 3 modulo 5 is any integer a such that 3 a ≡ 1 (mod 5), hence for some a ∈ Z5.Do such inverses exist for each element of Z5? If not, which ones?

A multiplicative inverse of 3 modulo 5 is any integer a such that 3 a ≡ 1 (mod 5), hence for some a ∈ Z5.

Do such inverses exist for each element of Z5? If not, which ones?