All about flooble | fun stuff | Get a free chatterbox | Free JavaScript | Avatars
 perplexus dot info

 Positive Integer, Odd Digits, Divisibility (Posted on 2013-05-12)
Prove that for each positive integer n, there exists an n-digit number having only odd digits and divisible by 5^n

 No Solution Yet Submitted by Danish Ahmed Khan Rating: 3.6667 (3 votes)

Comments: ( Back to comment list | You must be logged in to post comments.)
 re: Trials | Comment 3 of 5 |
(In reply to Trials by Salil)

The following extended table shows the odd-digited number growing from right to left, maintaining the same trailing digits as the preceding minimum such number.

` n       5^n               n-digit number          multiple of 5^n 1       5                 5                       1       2       25                75                      3       3       125               375                     3       4       625               9375                    15       5       3125              59375                   19       6       15625             359375                  23       7       78125             3359375                 43       8       390625            93359375                239       9       1953125           193359375               99       10      9765625           3193359375              327      11      48828125          73193359375             1499       12      244140625         773193359375            3167       13      1220703125        3773193359375           3091       14      6103515625        73773193359375          12087       15      30517578125       773773193359375         25355       16      152587890625      5773773193359375        37839       17      762939453125      15773773193359375       20675       18      3814697265625     515773773193359375      135207       19      19073486328125    7515773773193359375     394043       20      95367431640625    97515773773193359375    1022527       21      476837158203125   397515773773193359375   833651      22      2384185791015625  7397515773773193359375  3102743               23      11920928955078125 37397515773773193359375 3137131              `

produced by the following:

10   for N=1 to 23
20     B=5^N:Num=B:Mini=10^(N-1):Maxi=10^N-1:Found=0
30     repeat:Good=0
40      if Num>Mini then
50        :S=cutspc(str(Num))
60        :Good=1
70        :for I=1 to len(S)
80          :if val(mid(S,I,1))@2=0 then Good=0:endif
90        :next
100        :if Good then print N,B,Num,Num//B:endif
110      Num=Num+B
120     until Good=1 or Num>Maxi
130   next N

(with columns aligned manually)

 Posted by Charlie on 2013-05-13 08:55:27

 Search: Search body:
Forums (0)