1answer.
Ask question
Login Signup
Ask question
All categories
  • English
  • Mathematics
  • Social Studies
  • Business
  • History
  • Health
  • Geography
  • Biology
  • Physics
  • Chemistry
  • Computers and Technology
  • Arts
  • World Languages
  • Spanish
  • French
  • German
  • Advanced Placement (AP)
  • SAT
  • Medicine
  • Law
  • Engineering
Diano4ka-milaya [45]
3 years ago
13

Recall that the primes fall into three categories: Let Pi be the set of

Mathematics
1 answer:
a_sh-v [17]3 years ago
4 0

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

You might be interested in
If Asher plays each of the remaining seasons for which he is eligible, what is the average number of doubles he needs to hit per
PtichkaEL [24]

Answer:

the

Step-by-step explanation:

6 0
3 years ago
Kurt has a collection of 155 United States and Canadian stamps. He has 1.5 times as many United States stamps as Canadian stamps
stealth61 [152]

Kurt has 93 United States stamps in his collection

Step-by-step explanation:

The given is:

  • Kurt has a collection of 155 United States and Canadian stamps
  • He has 1.5 times as many United States stamps as Canadian stamps

We need to find how many United  States stamps Kurt has in his collection

Assume that kart has x Canadian stamps

∵ kart has x Canadian stamps

∵ He has 1.5 times as many United States stamps as Canadian stamps

- That means the number of United States stamps is 1.5 times

   the number of the Canadian stamps

∴ The number of the United States stamps = 1.5 x

∵ Kurt has a collection of 155 United States and Canadian stamps

- Add the two numbers of stamps and equate the answer by 155

∴ x + 1.5 x = 155

- Add like terms

∴ 2.5 x = 155

- Divide both sides by 2.5

∴ x = 62

∵ The number of United States stamps = 1.5 x

∴ The number of United States stamps = 1.5(62)

∴ The number of United States stamps = 93 stamps

Kurt has 93 United States stamps in his collection

Learn more:

You can earn more about the simple equation in brainly.com/question/11306893

#LearnwithBrainly

5 0
3 years ago
The population of medfield is 7000 Capitol City's population is 8/25 of Medfields what is capitol city's population
Dmitry_Shevchenko [17]
8/25 of medfield....." of " means multiply

8/25(7000) = 56,000/25 = 2240 <== capital city's population
5 0
3 years ago
What would gcf mean in your own words
padilas [110]
Greatest common fator

5 0
2 years ago
Solve 5^3x+1 = 4^x-5 for x
tensa zangetsu [6.8K]

For the equation 5^{3x+1}=4^{x-5} take the \log from both sides:

\log 5^{3x+1}=\log 4^{x-5},\\ \\(3x+1)\log 5=(x-5)\log 4.

Find x:

3x\log 5+\log 5=x\log 4-5\log 4,\\ \\3x\log 5-x\log 4=-5\log 4-\log 5,\\ \\x(3\log 5-\log 4)=-5\log 4-\log 5,\\ \\x=\dfrac{-5\log 4-\log 5}{3\log 5-\log 4}=\dfrac{5\log 4+\log 5}{\log 4-3\log 5}.

Answer: correct choice is D

7 0
3 years ago
Read 2 more answers
Other questions:
  • A jacket is on sale for 20% off the regular price. The sale price ism$50.00. What is the regular price of the jacket?
    15·2 answers
  • Is 61 divisible by 4?
    12·1 answer
  • August hosted two dinner parties for his friends. Twenty-five guests attended the first party, and twenty-six guests attended th
    5·1 answer
  • Find the length of side BC.
    13·1 answer
  • I need help with this.<br><br> please show me how you do it
    6·1 answer
  • Set up the equations to determine x and y.. help please
    6·1 answer
  • You sold your friend a raffle ticket for $1. If his ticket is selected from the 1000 sold, he will win
    13·1 answer
  • Solve this equation for x 2/3(x-7=-2
    8·2 answers
  • WILL MARK U BRAINLIEST
    6·1 answer
  • Identify the TRUE statement relating to a property of the function y = sin x
    13·1 answer
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!