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:
2x for the first term
The whole thing is 2x+3
Step-by-step explanation:
Think of it like normal division
What will get the closest answer to 2x^2+x?
2x*x-1=2x^2-2x
Now the expression is 3x-3 so if you but 3 than it becomes 3x-3 which would be a remainder of 0
Answer:
0.5
Step-by-step explanation:
you just need see at one point. i see at point (1, 0.5)
Answer:
$4020.52
Step-by-step explanation:
The future value is the principal multiplied by the amount $1.00 is worth in the future.
$4,000 × 1.00513 = $4020.52
Answer: 8 hours
Step-by-step explanation: he gets 70.40$ to work for 4 hours so you'll have to multiply 4 by 70.40 to represent it's doubling to 8 and you'll get 281.60
70.40x4=281.60
so add this 4 to the other 4 it makes 8 because that's how much it would take to get there 4 steps up to really =8
i'm sooo dificult