Let p be a prime. If the repeating decimal for the fraction a/p has even period, the second half of the decimals are the 9’s complement of the first half. This is known as Midy’s theorem. For a small example, take 1/7 = 0.142857142857… and notice that 142 + 857 = 999. That is, 8, 5, and […]
A while back I wrote about a method to test whether a number is divisible by seven. I recently ran across another method for testing divisibility by 7 in Martin Gardner’s book The Unexpected Hanging and Other Mathematical Diversions. The method doesn’t save too much effort compared to simply dividing by 7, but it’s interesting. It looks […]
“Casting out nines” is a trick for determining the remainder when a number is divided by nine. Just add the digits of the number together. For example, what’s the remainder when 3679 is divided by 9? The same as when 3+6+7+9 = 25 is divided by 9. We can apply the same trick again: 2+5 […]
I’ve mentioned base 64 encoding a few times here, but I’ve left out a detail. This post fills in that detail. Base 64 encoding comes up in multiple contexts in which you want to represent binary data in text form. I’ve mentioned base 64 encoding in the context of Gnu ASCII armor. A more common […]
One life-lesson from math is that sometimes you can solve a problem without doing what the problem at first seems to require. I’ll give an elementary example and a more advanced example. The first example is finding remainders. What is the remainder when 5,000,070,004 is divided by 9? At first it may seem that you […]
