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:
B) 6.5 inches by 3.5 inches
Step-by-step explanation:
Multiplying the actual dimensions by the scale gives the scale dimensions:
(0.5 in)/(6 ft) × {78 ft, 42 ft}
= {39/6 in, 21/6 in}
= {6.5 in, 3.5 in}
The size on the scale drawing is 6.5 inches by 3.5 inches.
Xy^16 / 4
I don't really know how to explain it, but this is the answer
Answer:
A full circle is 360 degrees so 2/3 is 120
Step-by-step explanation:
Answer: $1008
Step-by-step explanation:
Since Dave can only drive 35 miles per day and he drives 1,960 miles, this means that the number of days he used for driving will be:
= 1960 / 35
= 56 days
Since he gets paid $18 per day, the amount that he will make will be:
= $18 × 56
= $1008
