Hello, I would like to ask you to check if my assumption is correct:

In the context of the congruence and arithmetic:

5 * j = 1 (mod 2)

Now in order to solve this equation, Lenin (2019) says that we need to look at the greatest common divisor.

To do so, still, according to examples from Lenin (2019), we need to be able to divide both sides by 2, but before we need to add 2 to the right side until will become divisible by 2:

5j = 1 + 2 + 2 (mod 2)

5j = 5 (mod 2)

j = 5 (mod 2)

j = 11 (either 11 and 5 have the same remainder when divided by 2)

Below is the entire exercise I made:

1. Pick two prime numbers, P and 9. p = 2 and q = 3 2. Calculate n = P . q. n = 2 *3 = 6 3. Calculate 2 = (p - 1) . (q - 1). The z is often called "totient". Z = (p - 1) * (q - 1) = (2-1) * (3-1) z = 1 * 2 = 2 totient 4. Chose a prime number k so that & is co-prime to z (meaning, z is not divisible by k). k = 5 5. Take note of n and k, you will need them later. n = 6 and k = 5 6. Now, use the following equation to calculate | k . j = 1 (mod z) k * j = 1 (mod z) 5 * j = 1 (mod 2) Now in order to solve this equation, Lenin (2019) says that we need to look at the greatest common divisor. So do so, still according to examples from Lenin (2019), we need to be able to divide both sides by 2, but before we need to add 2 to the right side until will become divisible by 2: 5j = 1 + 2 + 2 (mod 2) 5j = 5 (mod 2) j = 5 (mod 2) J = 11 _(either 11 and 5 have the same reminder when divided by 2)