Find $4^{-1} \pmod{35}$, as a residue modulo 35. (Give an answer between 0 and 34, inclusive.)

We can use the Extended Euclidean algorithm to find the modular multiplicative inverse of 4 mod 35.

gcd(4, 35) = 1 4*11 - 35*1 = 1 11 is the modular multiplicative inverse of 4 mod 35.

Therefore, the multiplicative inverse of 4 mod 35 is 11.