B=1.4
Is the answer.
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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
Let x be the entire portion of the money Becca needs to save to buy a new tennis racket.
So, 0.25x=$21
x=$21/0.25
x=$84
Thus, the total amount she needs to save is $84. Now, we'll deduct 25 from 84 to get the 75 percent or the remaining amount she has to save.
$84-$21=$63
The answer is $63.
