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 Eleven Exponent Divides Evenly (Posted on 2009-08-01)
M is a 2003-digit positive decimal integer having the form: 12.....21
where, the first digit is 1, followed by the digit 2 repeated precisely 2001 times, and the last digit is 1.

Determine the highest power of 11 that evenly divides M.

 See The Solution Submitted by K Sengupta No Rating

Comments: ( Back to comment list | You must be logged in to post comments.)
 re(2): Solution verification by computer Comment 3 of 3 |
(In reply to re: Solution by Charlie)

10   B=1
20   for I=1 to 2001
30     B=B*10+2:N=10*B+1
40     Num=N:Ct=0
50     while (Num@11=0)
60       Ct=Ct+1
70       Num=Num//11
80     wend
90     print I;Ct
100   next

ends with:

. . .

`1975  21976  11977  21978  11979  31980  11981  21982  11983  21984  11985  21986  11987  21988  11989  21990  11991  21992  11993  21994  11995  21996  11997  21998  11999  22000  12001  3`
` `
`confirming the solution.`

 Posted by Charlie on 2009-08-01 16:30:59

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