Five years ago, I discussed some mathematics in Bad Luck and Trouble. I complained that suddenly, a new characteristic of Reacher was unveiled: he was a gifted mental calculator who could determine the primality of numbers quickly, and he was interested in properties like 'square root of n equals sum of n's base-10 digits'.
Now, in the new Reacher novel, A Wanted Man, Child returns to this numerological interest of his main character. First, Reacher is thinking about automorphic numbers: these are positive integers n such that n2 ends in the same base-10 digits as n.
Then (on page 64), Reacher is thinking about 81, and he "muse[s] about how one divided by 81 expressed as a decimal came out as .0123456789, which then recurred literally forever, 0123456789 over and over and over again..."
The problem? That's not the decimal expansion of 1/81. It's actually 0.012345679012345679012345679012345679012345679012345679012345679 ..., where the period of the expansion is 012345679 and not 0123456789. The "8" is missing! The reason for this is not so surprising, and generalizes easily to the expansion of 1/(n - 1)2 in base n.
A savant like Reacher, who can determine the closest prime to a randomly-chosen 6-digit number in a matter of a few seconds, would not have made such a silly mistake. Maybe Lee Child needs a mathematical consultant for his next novel. Hey, I'm available.