Number theory divisibility question

In summary, number theory is a branch of mathematics that studies the properties and relationships of numbers, particularly integers. Divisibility is the property of a number being able to be divided by another number without leaving a remainder. A divisibility question is a question that asks whether a given number is divisible by another number without leaving a remainder. In number theory, divisibility is tested using division and checking for a remainder. If the remainder is 0, then the numbers are divisible. Divisibility is an important concept in number theory as it helps identify patterns and relationships between numbers and has practical applications in fields such as cryptography and coding theory.
  • #1
Idiotinabox
3
0
Let a, b and c be positive integers such that a^(b+c) = b^c x c Prove that b is a divisor of c, and that c is of the form d^b for some positive integer d.

I'm not sure how to solve this question at all, I need some help.
 
Physics news on Phys.org
  • #2
Hey Idiotinabox.

Have you come across logarithmic congruence relations? Is there a way to use with the added constraint of c MOD b = 0?
 
  • #3
No, I have not come across them before. Could you elaborate?
 

Related to Number theory divisibility question

1. What is number theory?

Number theory is a branch of mathematics that studies the properties and relationships of numbers, particularly integers.

2. What is divisibility?

Divisibility is the property of a number being able to be divided by another number without leaving a remainder.

3. What is a divisibility question?

A divisibility question is a question that asks whether a given number is divisible by another number without leaving a remainder.

4. How is divisibility tested in number theory?

In number theory, divisibility is tested using division and checking for a remainder. If the remainder is 0, then the numbers are divisible.

5. What is the significance of divisibility in number theory?

Divisibility is an important concept in number theory as it helps identify patterns and relationships between numbers. It is also used in various mathematical proofs and has practical applications in fields such as cryptography and coding theory.

Similar threads

Replies
9
Views
1K
  • Linear and Abstract Algebra
2
Replies
55
Views
4K
  • Linear and Abstract Algebra
Replies
8
Views
1K
  • Linear and Abstract Algebra
Replies
8
Views
2K
  • Linear and Abstract Algebra
Replies
4
Views
1K
  • Linear and Abstract Algebra
Replies
8
Views
908
  • Linear and Abstract Algebra
Replies
3
Views
805
  • Linear and Abstract Algebra
Replies
9
Views
608
  • Linear and Abstract Algebra
Replies
7
Views
1K
  • Linear and Abstract Algebra
Replies
17
Views
1K
Back
Top