Dvisibility of large numbers

Therefore, 617+ 176 is not divisible by 3.In summary, the conversation discusses the divisibility of 6^17 + 17^6 by 3 or 7 and uses equations such as Fermat's little theorem to prove that it is not divisible by 3. The conversation also mentions the importance of prime numbers in this concept.
  • #1
lordy12
36
0
1. 6^17 + 17^6 is divisble by 3 or 7?

Homework Equations


3. 6^1 = 0(mod 3)
(6^1)^17=0(mod 3) so 6^17 is divisible by 3
how do u do this?
 
Last edited:
Physics news on Phys.org
  • #2
17 to any power is prime... No.

What is the stray T in your first line. Where did 61 come from? Why are you raising it to the power 1?
 
  • #3
sorry i changed it
 
  • #4
Fermat's little theorem.
 
  • #5
lordy12 said:
1. 6^17 + 17^6 is divisble by 3 or 7?



Homework Equations





3. 6^1 = 0(mod 3)
(6^1)^17=0(mod 3) so 6^17 is divisible by 3
how do u do this?

For 3 at least, you don't need anyone as powerful as Fermat! Suppose 617+ 176 were divisible by 3. Then we would have 617+ 176= 3n for some integer n. Then 176= 3n- 617= 3n- 317217= 3(n- 316217) which is impossible: since 17 is prime, no power of 17 is divisible by 3.
 

1. How is the visibility of large numbers determined?

The visibility of large numbers is determined by the number of digits in the number. Generally, numbers with more digits are considered to have lower visibility because they are harder to comprehend and visualize.

2. What is the significance of the visibility of large numbers?

The visibility of large numbers is important because it affects our ability to conceptualize and understand the magnitude of these numbers. It also impacts how we make decisions and evaluate risks based on these numbers.

3. How do we improve the visibility of large numbers?

One way to improve the visibility of large numbers is by using visual aids such as graphs, charts, and diagrams. Breaking down the number into smaller, more manageable units can also help improve visibility.

4. Are there cultural or personal factors that can influence the visibility of large numbers?

Yes, cultural and personal factors can play a role in how we perceive and understand large numbers. For example, individuals from cultures that do not use the decimal system may have more difficulty comprehending large numbers with many decimal places.

5. How does the visibility of large numbers impact scientific research and communication?

The visibility of large numbers can greatly impact scientific research and communication. It is important for scientists to present numbers in a way that is easily understandable to the general public, as well as other researchers in their field. This can help prevent misunderstandings and promote accurate interpretation of data.

Similar threads

  • Calculus and Beyond Homework Help
Replies
1
Views
1K
  • Calculus and Beyond Homework Help
Replies
7
Views
2K
  • Calculus and Beyond Homework Help
Replies
10
Views
752
  • Calculus and Beyond Homework Help
Replies
6
Views
1K
  • Calculus and Beyond Homework Help
Replies
6
Views
984
  • Calculus and Beyond Homework Help
Replies
7
Views
772
  • Calculus and Beyond Homework Help
Replies
16
Views
2K
  • Calculus and Beyond Homework Help
Replies
14
Views
729
  • Calculus and Beyond Homework Help
Replies
30
Views
2K
  • Calculus and Beyond Homework Help
Replies
6
Views
589
Back
Top