Yes, 101 and 4620 are coprime (their only common factor is 1), so the multiplicative inverse of 101 mod 4620 exists. We can easily verify that it equals 1601, because 101 × 1601 ≡ 161701 and 161701 = 4620 × 35 + 1; that is, 101 × 1601 = 1 (mod 4620 ). However, while verification is easy, finding the result in the first place requires using the extended Euclidean algorithm. Read more