حل هر مشکل ریاضی

قدم به قدم

1. 4x \equiv 1 \pmod{9}

   We want x with a·x ≡ 1 (mod m). It exists only when gcd(a, m) = 1.

2. 9 = 2 \times 4 + 1

   Euclid step.

3. 4 = 4 \times 1 + 0

   Euclid step.

4. 4 \times 7 = 28 \equiv 1 \pmod{9}

   Back-substitute (extended Euclid) to express 1 as a combination of a and m; the coefficient of a is the inverse.

جواب رو نشون بده

4^{-1} \equiv 7 \pmod{9}