Timeline for Combinatorial meaning of a reduced fraction in a simple probability problem?
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| Jul 2, 2023 at 21:24 | comment | added | Michael Hardy | $\ldots\,$never studied $p$-adic numbers. Right now I'm wondering how much of your answer survives if you omit the mentions of $v_p$ and keep everything you've said about $\alpha_p. \qquad$ | |
| Jul 2, 2023 at 21:22 | comment | added | Michael Hardy | As far as I recall at the moment, the only occasion I've had to think about the sum of base-something digits of an integer (when it wasn't some silly puzzle) is in the fact that the sum of the base-10 digits of an integer is congruent modulo 3 to the integer itself, and similarly with 9 instead of 3. Since 10 is not prime, some things may be different. Your statement implies that the sum of the base-$p$ digits of $n$ is congruent to $n$ modulo $p-1.$ Maybe everyone knows that except me. My unawareness of the first equality in your answer is explained by the fact that I've$\,\ldots\qquad$ | |
| Jul 2, 2023 at 19:16 | history | answered | Neil Strickland | CC BY-SA 4.0 |