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
90 is the largest integer
Answer:
2 1/3 cupcakes
Step-by-step explanation:
A cupcake can make 3 four cups of flour
In 8 fourteen cups of flour, require (14 X 4)/(3 X 8) of cupcakes
= 56/24 = 2 1/3 cupcakes
Answer:
The domain would be given by <u>D = {X ≥ 2} X = [2, Z].</u> Since the variable Z is the number of children in the school. And the 6 children should not survey the same person, it would be Z / 6 for each interviewer.
Step-by-step explanation:
- If the group of children surveys more than 2 classmates, it means that the number with which the survey begins is 12 students.
And since the maximum number of students in the school is given by the variable of Z, then Z is the number with which the domain closes.
The rank would be given by the set of [2, Z]
Z / 6 being the maximum number of children surveyed by 1 interviewer.
Answer:
left to right
yes no no no yes yes yes yes yes yes yes no
Step-by-step explanation:
the x values can only have 1 y
Y's can have as many X's
