Modulo Arithmetic/Examples/Multiplicative Inverse of 41 Modulo 97/41x = 2 Modulo 97

Example of Modulo Arithmetic
The solution of the integer congruence:
 * $41 x \equiv 2 \pmod {97}$

is:
 * $x = 45$

Proof
From Multiplicative Inverse of $41 \pmod {97}$ we have:
 * $41 \times 71 = 1 \pmod {97}$

Thus:

Hence the result.