- #1
Natasha1
- 494
- 9
Without using a calculator, how can I know if 5 is a divisor of 3^444 and/or 4^333?
Is 5 a divisor of 3^444 & 4^333?
- Thread starter Natasha1
- Start date
Click For Summary
Homework Help Overview
The discussion revolves around determining whether 5 is a divisor of the expressions 3^444 and 4^333, focusing on concepts related to prime factorization and divisibility.
Discussion Character
- Exploratory, Conceptual clarification, Assumption checking
Approaches and Questions Raised
- Participants explore the relevance of prime factorization and Fermat's Little Theorem in assessing divisibility. There are questions about the application of these concepts to the specific powers of 3 and 4.
Discussion Status
The conversation is ongoing, with participants sharing insights about prime factorization and its implications for the problem. Some guidance has been offered regarding the unique representation of numbers as products of primes, but no consensus has been reached.
Contextual Notes
There is a mention of potential misunderstandings regarding the problem setup and the need for clarity on prime factorization concepts. The original poster's request for a non-calculator approach suggests constraints on the methods discussed.
- #2
matt grime
Science Advisor
Homework Helper
- 9,361
- 6
Fermat's Little theorem, how else can you say anything about anything?
- #3
Manchot
- 470
- 5
Did you learn about prime factorization in grade school? 
- #4
matt grime
Science Advisor
Homework Helper
- 9,361
- 6
true, i misread it.
- #5
Natasha1
- 494
- 9
Manchot said:Did you learn about prime factorization in grade school?
No...
- #6
HallsofIvy
Science Advisor
Homework Helper
- 42,895
- 983
Well, you should have! Any number can be written, in a unique way, as a product of primes. How would 3444 be written as a product of primes? Any 5s in there? (Hint: 3 and 5 are prime numbers.)
How would 4333 be written as a product of primes? (Hint: 4 is not a prime number but 2 is.)
How would 4333 be written as a product of primes? (Hint: 4 is not a prime number but 2 is.)