What is unusual about the # 1634?

Originally posted by sonhouse
Regular base 10 number, nothing tricky there. 1634, what makes it unusual?

ohhhhhhhh! that's my rating!!!

Originally posted by geepamoogle
The mathematical property of being exactly one more than 1633?

I did factor it, and 1634 = 2 * 19 * 43. Not sure if that sheds any light on the particular uniqueness though.

The unique-ness is simply this -

1634 = 1^4 + 6^4 + 3^4 + 4^4. ( no. of digits in the no is 4).

Originally posted by howzzat
The unique-ness is simply this -

1634 = 1^4 + 6^4 + 3^4 + 4^4. ( no. of digits in the no is 4).

So [abcd] is a number that can be described as a^4 + b^4 + c^4 + d^4. The only [abcd] that can be described in this way is 1634.

Can you prove this uniqueness?

Let's call the example above having order 4 as it's having 4 figures in its number. What about any other order?

Like in order 5: Is there a number [abcde] that can be described as a^5 + b^5 + c^5 + d^5 + e^5?

Oh Dear! The number 42 may actually be threatened here.

Originally posted by howzzat
The unique-ness is simply this -

1634 = 1^4 + 6^4 + 3^4 + 4^4. ( no. of digits in the no is 4).

What about the numbers 8208 and 9474? 🙂

Edit: Other than the fact that 1634 is also 4 unique digits?

Originally posted by FabianFnas
So [abcd] is a number that can be described as a^4 + b^4 + c^4 + d^4. The only [abcd] that can be described in this way is 1634.

Can you prove this uniqueness?

Let's call the example above having order 4 as it's having 4 figures in its number. What about any other order?

Like in order 5: Is there a number [abcde] that can be described as a^5 + b^5 + c^5 + d^5 + e^5?

I believe that these are the [abcde] numbers:
54748
92727
93084

And that this is the only [abcdef] number:
548834

Originally posted by coquette
http://en.wikipedia.org/wiki/1634

http://www.stetson.edu/~efriedma/numbers.html

http://mathworld.wolfram.com/NarcissisticNumber.html

Whoops, beaten to it by a long way. 😳

Originally posted by sonhouse
Regular base 10 number, nothing tricky there. 1634, what makes it unusual?

that's the street address where "Malone" of the Untouchables lived.

1634 racine....(it was written inside the matchbook of his assassin)

Originally posted by uzless
that's the street address where "Malone" of the Untouchables lived.

1634 racine....(it was written inside the matchbook of his assassin)

So he wasn't quite as untouchable as he thought, eh.