What is the number of zeros in the decimal expansion of $11^{100}-1$?
Number of zeros in decimal expansion
0
$\begingroup$
elementary-number-theory
-
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
2 Answers
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.