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
We assume the two numbers are x and (x+1)
so x^2+(x+1)^2=421
x^2+(x^2+2x+1)=421
2x^2+2x-420=0
According to the formula of quadratic
x=14 or-15
cuz we know the two numbers are integers
so x=14
therefore the other number is 15
To make sure that's correct
14^2+15^2=421
Hope that helps you!!
Answer:
The correct answer is:
r + 0.50 = 10.25: Subtract .50 from both sides. The answer is $9.75.
This is because Juan got a $0.50 raise which means that his new rate will be $0.50 more than his original rate (r).
Answer:
3,000
Step-by-step explanation:
6:5
1.2( divided 6 by 5):1 (Divide 5 by 5)
3600 divided by 1.2
3,000
I hope this helps!
25 is 7.8
26 is 8.3
27 is 14.5
28 is yes, they both ran the same distance because 7×5 is equal to 5×7. They both equal 35. So, both ran the same distance.
