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
emmasim [6.3K]
3 years ago
7

Determine the greatest common divisor of the elements of the set \[ s = \{ n^{13} - n \mid n \in \mathbb{z} \}. \]

Mathematics
1 answer:
Kay [80]3 years ago
5 0

Answer:

2730

Step-by-step explanation:

We want to determine the greatest common divisor of the elements of the set  S = \{ n^{13} - n \mid n \in \mathbb{Z} \}.

We apply the Fermat's little theorem which states that if p is a prime number, then for any integer a, the number aᵖ − a is an integer multiple of p.

Now, n^{13} \equiv n \mod p if p-1 divides 12.

Since the  of 12 are 1,2,3,4, 6, 12, the corresponding primes are 2, 3, 5, 7, 13.

Therefore, the gcd of the elements in 2^{13}-2 and 3^{13}-3$ is 2 \cdot 3 \cdot 5 \cdot 7 \cdot 13.

2*3*5*7*13=2730

Therefore, the gcd of the elements in set S is 2730.

You might be interested in
The sum of a number and 9, times 12
Sliva [168]

Answer:

1 + 9 x 12 = 120

2 + 9 x 12 = 132

3 + 9 x 12 = 144

4 + 9 x 12 = 156

5 + 9 x 12 = 168

Step-by-step explanation:

Any of the ones on top, but there are tons of others too

6 0
3 years ago
A fenced-in rectangular area has a perimeter of 40 ft. The fence has a post every 5 ft.
sertanlavr [38]
8 post 4ft is the length 2ft ,yes if you dived 5 from 40 that is how many post , then you dived how many posts and that is the  height then you dvide that and that is your width.

7 0
3 years ago
What is the image of the point (-6,2) after a 90 degree counterclockwise rotation
Gala2k [10]
The answer is (-2, -6)
to rotate 90 degrees counterclockwise, you do (-y, x)
5 0
3 years ago
6x + 10x = 64 what does x equal?
Nutka1998 [239]
X= 4
You add 6x and 10x then divide 16x from 64 which makes x=4
6 0
3 years ago
Read 2 more answers
7. It is best to save _____ months of fixed expenses for an emergency fund. (1 point)
patriot [66]
I think the best answer is 3 to 9 but thats not a answer so 3 to 6
5 0
3 years ago
Read 2 more answers
Other questions:
  • What is the value of (1)?
    7·2 answers
  • Help!!! <br><br> 2x+3=6 solve for x
    6·2 answers
  • Jeremy uses the linear function G = 12h + 50 to represent the grade, G (in points out of 100), that he can earn on an exam as a
    14·1 answer
  • How many thousands does 0.572 represent
    11·2 answers
  • Here are some questions I'm confused about
    10·2 answers
  • You are given the equation (2x^ny^2)^m = 4x^6y^4. Find two positive​ integers, m and​ n, that make the equation true.
    10·1 answer
  • Plz answer I need help Plz
    10·1 answer
  • Please help me please​
    15·1 answer
  • Using the standard 28/36 guidelines, what is the maximum mortgage payment allowed for someone with an annual salary of $82,175?
    12·1 answer
  • I very much need help, please. This is trigonometry.
    10·1 answer
Add answer
Login
Not registered? Fast signup
Signup
Login Signup
Ask question!