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[murthy amarnath]

Dear all,
kindly look into this.
Is the following conjecture true?
(1): 3^r  divides  (10^k -1)/9   iff  3^r divides k.
(I verified  it to be true for  r = 1,2,3 and  4.)

Similarly
 (2): 11^r  divides  {10^(2k) -1}/9   iff  11^r
divides k.
  (3): 7^r  divides  {10^(6k) -1}/9   iff 
7^(r-1)divides k.

thanks
regards
amarnath murthy



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