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What is the number of zeros in the decimal expansion of $11^{100}-1$?

  • 1
    You 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

2 Answers 2

2

11^100 - 1 = 137806123398222701841183371720896367762643312000384664331464775521549852095523076769401159497458526446000 which has 12 zeros.

2

We ca see that,

$11^{100}-1=(10+1)^{100}-1=(10^{100}+100\cdot10^{99}+99\cdot50\cdot 10^{98}+...+1)-1$

Now, try to investigate the above.