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:
t=2x+ 2
Step-by-step explanation:
x is every phone call 2 is how many minutes she spends on each call The other 2 is the 2 minutes she already spended
Answer:
89 meters
Step-by-step explanation:
We know it's 9 + "the height of the triangle".
Fortunately, the height of the triangle (let's call it y) can be computed from:
y^2 + 18^2 = 82^2 (Pythagoras theorem).
y^2 = 82^2 - 18^2 = 6724 - 324 = 6400
y = 80 (or y = -80 but it doesn't make sense in geometry).
so x = y + 9 = 89;
11 3/5 - 5 19/20
58/5 - 5 19/20
58/5 - 119/20
113/20
= 5.65
I hope that's help ! If you have question(s) please let me know
