Question

2. The inverse of 3 modulo 7 is?​

Answer 1

SOLUTION

TO DETERMINE

The inverse of 3 modulo 7

CONCEPT TO BE IMPLEMENTED

Let m be a positive integer. For an integer a with gcd (a, m) = 1, an integer b is called an inverse of a modulo m if

$\sf{ab \equiv 1 \: (mod \: m \: )}$

From above it follows that b is an inverse of a modulo m if and only if b is a solution of the congruence

$\sf{ab \equiv 1 \: (mod \: m \: )}$

EVALUATION

Now we have to determine the inverse of 3 modulo 7

Since ( 3 × 5 ) - 1 is divisible by 7

$\therefore \: \: \sf{3.5 \: \equiv \: 1 \: (mod \: 7)}$

Hence 5 is the inverse of 3 modulo 7

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