Answer:
Check the explanation
Step-by-step explanation:
(a)Let p be the smallest prime divisor of (n!)^2+1 if p<=n then p|n! Hence p can not divide (n!)^2+1. Hence p>n
(b) (n!)^2=-1 mod p now by format theorem (n!)^(p-1)= 1 mod p ( as p doesn't divide (n!)^2)
Hence (-1)^(p-1)/2= 1 mod p hence [ as p-1/2 is an integer] and hence( p-1)/2 is even number hence p is of the form 4k+1
(C) now let p be the largest prime of the form 4k+1 consider x= (p!)^2+1 . Let q be the smallest prime dividing x . By the previous exercises q> p and q is also of the form 4k+1 hence contradiction. Hence P_1 is infinite
Answer:

Step-by-step explanation:
Let determine the angles behind each trigonometric expression:


Given that
, the value of
is:



Given that
, the value of
is:

The sine function of the sum of angles can be determined by the following identity:

If
and
, then:


Answer:

Step-by-step explanation:
In order to find the value of ∠EFB here, we have to note our angle relationships.
We know that ∠CFE is already 90°. We also know that ∠CFA is 90°. Angle ∠AFB is inside ∠CFA. Since we know the measure of ∠AFB, we can find the measure of ∠BFC.

Now that we know ∠CFE and ∠BFC, which together make ∠BFE, we can add these angles up.

Hope this helped!
Answer:
71/100
Step-by-step explanation:
Action 29 plus comedy 42 equals 71 and if you add action, comedy, drama, and horror you get your denominator of 100