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Is 5 a divisor of 3^444 & 4^333?

  1. Feb 21, 2006 #1
    Without using a calculator, how can I know if 5 is a divisor of 3^444 and/or 4^333?
     
  2. jcsd
  3. Feb 21, 2006 #2

    matt grime

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    Fermat's Little theorem, how else can you say anything about anything?
     
  4. Feb 21, 2006 #3
    Did you learn about prime factorization in grade school? :biggrin:
     
  5. Feb 21, 2006 #4

    matt grime

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    true, i misread it.
     
  6. Feb 22, 2006 #5
    No... :uhh:
     
  7. Feb 22, 2006 #6

    HallsofIvy

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    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.)
     
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