Question

43*(3/17) mod 11 using the a * a-1 = 1 mod m. Trying
to figure out how to do the calculations.

Answer 1

To compute 43*(3/17) mod 11, we first find the multiplicative inverse of 3 mod 17, which is 6. Multiplying 43 by 6 and taking the result modulo 11 yields the final answer, which is 5.

Step-by-step explanation:

The question asks to calculate the expression 43*(3/17) mod 11 using the multiplicative inverse property which states a * a^-1 ≡ 1 (mod m). To simplify the expression, we need to find a number that, when multiplied by 3, gives us a remainder of 1 when divided by 17 (the multiplicative inverse of 3 modulo 17). Once we have this number, we can multiply it with 43 and then take the result modulo 11 to get our final answer.

First, let's find the multiplicative inverse of 3 modulo 17. Since 3 * 6 ≡ 18 ≡ 1 (mod 17), we know that 6 is the multiplicative inverse of 3 mod 17. Now, we can replace (3/17) with 6 in our expression:

43 * 6 mod 11. We now compute this:

43 * 6 = 258

Now, taking this result modulo 11:

258 mod 11 = 5

Therefore, 43*(3/17) mod 11 equals 5.