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:
c
Step-by-step explanation:
Hope this helps.
Answer:
the answer of the question is b. 8.2 mm
Answer:
see below
Step-by-step explanation:
a) w <= 40 lbs
b) Do you have any bag that weigh 0 lbs or negative lbs?
We need to rewrite the inequality so that these are not there
0<= w <= 40 lbs
