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
That would be 4(16) - 8 - (4(0) - 8) = 64 - 9 - 0 + 8 = 63 Answer
Answer:
55
Step-by-step explanation:
Divide both sides by 3.14 to get d by itself.
172.7 / 3.14 = 55 = d
Answer:
B
Step-by-step explanation:
it shows every 4 hours, so:
560-336=224
224:4=56 per hour
Answer:
Step 1. The answer is no.
Step 2. The answer is b.
Step-by-step explanation:
I think Step 2 already sort of explains the reasoning behind the answer for step 1.
Hope this helps!
