What is the number of zeros in the decimal expansion of $11^{100}-1$?
Number of zeros in decimal expansion
0
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elementary-number-theory
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0According to python 12. Your number is 137806123398222701841183371720896367762643312000384664331464775521549852095523076769401159497458526446000. – 2012-10-25
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0how can it be solved using some theorems? – 2012-10-25
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0Or if that's binary, you have 3^4 - 1 = 80, so the answer is 1 zero in the decimal expansion. – 2012-10-25
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1You can easily show that $11^{100} - 1$ has exactly $3$ trailing $0$'s. However, the $0$'s in the middle of the number are not really very amenable to analysis. – 2012-10-25