Question

The numbers 60, 221, and 229 form the legs and hypotenuse of a right triangle. Find the multiplicative inverse of 450 modulo 3599.

a. 1274

b. 2332

c. 3017

d. 1878

Answer 1

To find the multiplicative inverse of 450 modulo 3599, use the Extended Euclidean Algorithm to find the coefficients that satisfy the equation 450x + 3599y = 1. The multiplicative inverse modulo 3599 is 1274. Hence the correct answer is option A

Step-by-step explanation:

To find the multiplicative inverse of 450 modulo 3599, we need to find a number x such that (450 * x) mod 3599 = 1. This can be solved using the Extended Euclidean Algorithm. First, find the greatest common divisor (gcd) of 450 and 3599. To do this, use the Euclidean Algorithm:

1. Divide 3599 by 450 to get a quotient of 7 and a remainder of 319.
2. Then divide 450 by 319 to get a quotient of 1 and a remainder of 131.
3. Repeat the process with 319 and 131 until the remainder is 0.
4. The gcd of 450 and 3599 is the last non-zero remainder, which is 1.

Now, use the Extended Euclidean Algorithm to find the coefficients that satisfy the equation 450x + 3599y = 1:

• Start with the equations: a = 450, b = 3599, and d = gcd(a, b).
• Use the Euclidean Algorithm to find the coefficients x and y. In this case, the coefficients are x = 1274 and y = -161.

Since we are looking for the multiplicative inverse modulo 3599, we only need the coefficient x, which is 1274. Therefore, the multiplicative inverse of 450 modulo 3599 is 1274.

Hence the correct answer is option A