SOLUTION: what is the remainder when 77777.... up to 37 terms is divided by 19? [ I can do it using the fermat's little theorem, is there any other formula using co-prime property betwe

Algebra ->  Divisibility and Prime Numbers -> SOLUTION: what is the remainder when 77777.... up to 37 terms is divided by 19? [ I can do it using the fermat's little theorem, is there any other formula using co-prime property betwe      Log On


   

Question 919965: what is the remainder when 77777.... up to 37 terms is divided by 19?
[ I can do it using the fermat's little theorem,
is there any other formula using co-prime property between 7 & 19? ]
Answer by Edwin McCravy(20056) About Me  (Show Source):
You can put this solution on YOUR website!
This is a special case, nothing in general at all. So why 
not show it like a 4th grader would show it?  By long division.  
As we can see from the long division below the remainders go:

7, 1, 17, 6, 10, 12, 13, 4, 9, 2, 8, 11, 3, 18, 16, 15, 5, 0,
7, 1, 17, 6, 10, 12, 13, 4, 9, 2, 8, 11, 3, 18, 16, 15, 5, 0,
   

    409356725146198830   
19)7777777777777777777
   76
    17
    00
    177
    171
      67
      57
      107
       95
       127
       114
        137
        133
          47
          38
           97
           95
            27
            19
             87
             76
             117
             114
               37
               19
               187
               171
                167
                152
                 157
                 152
                   57
                   57
                    0

Edwin