00:01
From the given question, to solve the congruence, 15x is equal to 12 into mod of 57.
00:16
Dividing, dividing both sides by 3.
00:24
Then 5x is equal to 4 into mod of 19.
00:30
Then we can find the modular inverse of 5 modulo 19 where which is integer k such that 5k is equal to 1 into mod 19.
01:05
Using euclidean algorithm, 19 is equal to 5 into 3 plus 4, 5 is equal to 4 into 1 plus 1, 1 is equal to 5 minus 4 into 1, 1 is equal to 5 minus minus bracket of 19 minus 5 into 3 into 1.
01:35
1 is equal to 5 into 4 minus 19 into 1.
01:40
Therefore, k is equal to 4.
01:45
Multiply both sides of congruence by k.
01:55
Then 5x is equal to 4 into mod 19.
02:04
That is equal to 20x is equal to 16 into mod 19.
02:09
Then simplify by using the congruence in the form of 20x is equal to 16 into mod 19.
02:35
That is equal to x is equal to 16 into mod 19.
02:40
So the solution of the congruence are x is equal to 16 plus 19k mod 57 where k is an integer.
03:07
K is an integer...