It is proved that C (m, n) can be divisible by n C (m, n) is the combination number of m from n, M

It is proved that C (m, n) can be divisible by n C (m, n) is the combination number of m from n, M

C(m,n) = n!/ (n-m)!m!= (n-m+1)...(n-1)n / m!
C (m, n) is an integer, so the denominator must divide the numerator;
If n is prime, n cannot be divided, so the factor of C (m, n) contains n;
That is, C (m, n) can be divisible by n
Note: here must satisfy the condition m < n, there is no equal sign

In number theory, it is known that positive integer m greater than 1 satisfies m | (m-1)! + 1. It is proved that M is prime

If M is a composite number, then M must divide some number in 2 ~ m - 1
But from the formula, m divided by 2 ~ M-1, any number remainder is 1
So m must be prime

M is a positive integer and M is greater than 3. How many primes are there at most among the six numbers from M + 1 to m + 6

2
Because there are three even numbers, one of the remaining three is divisible by three
Only 6-3-1 = 2 possible
And two are easy to find