15x= mod88
Trying to work out the inverse of this, so far using Euclids algorithm I've got the GCF as 1 but I'm not sure where to go from here. Anyone able to help?
To find the inverse of 15 modulo 88 using Euclid's algorithm, let's first review the steps.
1. Write the equation:
15x ≡ 1 (mod 88)
2. Apply Euclid's algorithm:
88 = 5 * 15 + 13
15 = 1 * 13 + 2
13 = 6 * 2 + 1
3. Work backward:
Start with the equation 1 = 13 - 6 * 2.
Substitute 2nd equation:
1 = 13 - 6 * (15 - 13) = 7 * 13 - 6 * 15.
Substitute 1st equation:
1 = 7 * (88 - 5 * 15) - 6 * 15 = -6 * 15 + 7 * 88.
Now we have 1 expressed in terms of −6 * 15 + 7 * 88. Therefore, the inverse of 15 modulo 88 is -6 (or 82, since -6 + 88 ≡ 82 (mod 88)).