NumberCatalog v1 - Trending Values - 2025/12/30

Today's trending values are 909, 808 and 707.

909's claim to fame

The number 909 is trending today after having appeared on 5 different sites, the number has been visited by 355 people!

Proof that 80 is equal to 808

The number 808 is a lot of fun, because of its powerset and how easy is to show that 80 is equal to 808! I remember from my childhood, that this is called the cube. Of course I knew, how easy this could be proved using modular arithmetic.

In 2009 I found the solution for it, when I had to solve a puzzle. But in the first place, I wanted to share, that the way of proving it could be very useful, and could lead you in interesting and cool puzzles, if you take some time to explore.

Since it is not very interesting to prove this with modular arithmetic, you can solve it, with brute force: Take powers of the digits 8 and 0 and try, how many digits of this number will have a cube in them.

Here the first digit can't have a cube (for instance, it could only have 0), but for the first and the third digit of 80, only the cube has to be at least 2. We only need to take the power of the second and the second to the 3rd, and compare.

You can try, how many cubes 0-7 has as cube.

2*4=8 and 2*5=10 is the cube of 8, since the sum is 12.

5*7=35 and 5*6=30, neither of them is 81.

2*6*3=36 is also not equal to 80.

The cubes have to have a sum, equal to 81.

The cubes only can be 32 and 81. If we only add them up, the first digit only can't have a cube.

And then only we can have, that only 1 is 81 (when only 5 is left for 8).