The canonical representative of15^11 mod3337
To find the canonical representative of 15^11 mod 3337, you can use modular exponentiation. Essentially, you'll be repeatedly multiplying 15 by itself, modulo 3337, for a certain number of times.
Here's a step-by-step process to find the answer:
1. Start by calculating 15^1 mod 3337. Since any number raised to the power of 1 is itself, the result is 15.
2. To calculate 15^2 mod 3337, square the result from the previous step (15) and then find its modulo 3337. It will be (15^2) mod 3337 = 225.
3. Continue this process for consecutive powers of 15 until you reach 15^11 mod 3337. Each time, take the previous result, multiply it by 15, and then take the modulo 3337.
15^3 mod 3337 = (225 * 15) mod 3337 = 3375 mod 3337 = 38
15^4 mod 3337 = (38 * 15) mod 3337 = 570 mod 3337 = 570
15^5 mod 3337 = (570 * 15) mod 3337 = 8550 mod 3337 = 1647
15^6 mod 3337 = (1647 * 15) mod 3337 = 24705 mod 3337 = 3024
15^7 mod 3337 = (3024 * 15) mod 3337 = 45360 mod 3337 = 213
15^8 mod 3337 = (213 * 15) mod 3337 = 3195 mod 3337 = 3195
15^9 mod 3337 = (3195 * 15) mod 3337 = 47925 mod 3337 = 458
15^10 mod 3337 = (458 * 15) mod 3337 = 6870 mod 3337 = 6870
15^11 mod 3337 = (6870 * 15) mod 3337 = 103050 mod 3337 = 15
So, the canonical representative of 15^11 mod 3337 is 15.