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Least positive rest in division?

  1. Sep 11, 2010 #1
    1. The problem statement, all variables and given/known data

    Find the least positive rest in division of 7^35 with 5

    2. Relevant equations


    3. The attempt at a solution

    7^35=378818692265664781682717625943 => 378818692265664781682717625943/5....... Uhhhhh this is not the way I am supposed to take right????? :cry:
  2. jcsd
  3. Sep 11, 2010 #2


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    Gold Member

    What does the phrase "least positive rest" mean? I did a brief google search on it and didn't find anything helpful.
  4. Sep 11, 2010 #3


    Staff: Mentor

    By "least positive rest" I think the OP means "remainder." Presumably properties of modular arithmetic should be used to find this remainder.

    For example, 7 [itex]\equiv[/itex] 2 (mod 5), so 735 [itex]\equiv[/itex] 235 (mod 5). Does any of this look familiar?
  5. Sep 12, 2010 #4
    I am sorry that I got you confused by the translation. Yes, as Mark44 mentioned, it means remainder.

    This is exactly what I am looking for and it looks familiar :)

    But I don't get how 7^35=2^35 (mod 5) Please explain?
  6. Sep 12, 2010 #5


    Staff: Mentor

    As I already explained, because 7 (mod 5) [itex]\equiv[/itex] 2 (mod 5), then 735 (mod 5)[itex]\equiv[/itex] 235 (mod 5).
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