A number N consisting of a string of sevens i.e. N=77777...7777, is divisible by 199. Find the last 4 digits of the quotient. No programming, please.

(In reply to Such a number exists. by Jer)

Indeed there are 99 7's in N, shown below, followed by the quotient and the common log of N verifying its 99-digit length.

list
    5   N=7
   10   while N@199>0
   20       N=N*10+7
   30   wend
   40   print N
   50   print N//199
   60   print log(N)/log(10)
OK
run
 7777777777777777777777777777777777777777777777777777777777777777777777777777777
77777777777777777777
 3908431044109436069235064209938581797878280290340591848129536571747627024008933
556672250139586823
 98.8908555305749319713
OK

Posted by Charlie on 2010-02-05 16:47:53