00:01
Hello, let's have a look at the question.
00:02
So here it is given for n is greater than equals to 2, n divides n minus 1 factorial plus 1.
00:15
That means n divides n minus 1 factorial plus 1.
00:21
Now let us take this as first equation.
00:25
Now we have to prove n is prime.
00:30
So we will prove this by contradiction.
00:41
Suppose n is not a prime number.
00:55
So now let us take that let n is equals to a into b for some a belongs to value 1 to n and b and b also lies from 1 to n.
01:17
To 2 to n minus 1 that is 1 is less than a and which is less than n.
01:29
So here we can say that a divides the product of this series that is n minus 1 factorial.
01:38
So let us take this as second equation.
01:41
Now we also know that n is equals to a into b.
01:46
So here we can say that a divides ab, that is here we can write a divides n...