25 Dec 08
Originally posted by geepamoogleThe unique-ness is simply this -
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.
1634 = 1^4 + 6^4 + 3^4 + 4^4. ( no. of digits in the no is 4).
27 Dec 08
Originally posted by howzzatSo [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.
The unique-ness is simply this -
1634 = 1^4 + 6^4 + 3^4 + 4^4. ( no. of digits in the no is 4).
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?
05 Jan 09
Originally posted by FabianFnasI believe that these are the [abcde] numbers:
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?
54748
92727
93084
And that this is the only [abcdef] number:
548834