## To the Ninth Power

5^{9} + 3^{9} + 4^{9} + 4^{9} + 9^{9} + 4^{9} + 8^{9} + 3^{9} + 6^{9} = 534494836

## Münchhausen Numbers

Münchhausen number is a number equal to the sum of its nonzero digits raised to each digit’s power. There are only two of these numbers besides the trivial 0 and 1. See A046253.

3435 = 3^{3} + 4^{4} + 3^{3} + 5^{5}

438579088 = 4^{4} + 3^{3} + 8^{8} + 5^{5} + 7^{7} + 9^{9} + 0^{0} + 8^{8} + 8^{8}

## The Number 1729

According to the Indian mathematican Srinivasa Ramanujan, “[1729] is a very interesting number; it is the smallest number expressible as the sum of two cubes in two different ways.” It can be expressed as:

1729 = 1^{3} + 12^{3} = 9^{3} + 10^{3}

In addition, if you add the number of the beast (666) to 1729, the total is equal to the sum of the first prime number (2) and the squares of the next nine consecutive primes.

1729 + 666 = 2 + 3^{2} + 5^{2} +7^{2} + 9^{2} + 11^{2} + 13^{2} + 17^{2} + 19^{2} + 23^{2} + 29^{2 }= 2395

I have skimmed some writings on numerology and the mystical sides of numbers like 9 and 7 but never really followed it up. To the Ninth power seems to feature this 9 again. So much to learn.

LikeLiked by 1 person

There are many things said about those two numbers in both Eastern and Western numerology.

LikeLiked by 1 person

Aagghh, jumps up from chair and runs from the room…

LikeLiked by 2 people

mathematics can be so fascinating

LikeLiked by 1 person

Yes.

LikeLiked by 1 person

As a math dummy I’m not sure which is more amazing, the numbers or the people who discovered them.

LikeLiked by 2 people

I’m glad to hear that. Not many people praise this kind of thing. Some even say that it’s just a waste of time. To each his own I suppose.

Anyway, I was the one who found the one with the ninth powers (using Python) and the 1729 + 666 one by accident. I don’t claim that I am the first one who found these properties as I suspect that these are already known before. 😀

LikeLiked by 2 people

If I remember correctly, the story about 1729 is that Ramanunjan was visited by his mathematician friend Hardy who arrived in a cab. Hardy saw the number 1729 on it, and said, “Well nothing interesting there.” Ramanunjan instantly replied, on the spot, “No it’s the smallest number expressible as the sum of two cubes.” Hardy was dumbfounded that this formally uneducated man had had such a profound grasp of mathematics.

LikeLiked by 1 person

Hmm, that should be, “No, it’s the smallest number expressible as the sum of two cubes in two distinct ways.”

LikeLiked by 1 person

I first read it on Hardy’s A Mathematician’s Apology.

LikeLike

I enjoyed the information. All of it is way beyond my comprehension, but I like to think I know and understand it. There are just some things you have to just believe.

LikeLike