Question

Find a four-digit number such that it equals to the third power of the sum of all of its integers

Answer 1

I guess not hit and trial method??

Answer 2

prof!!!!!

Answer 3

This like the problem posted by @Callisto
It gas two solutions.

Answer 4

has not gas

Answer 5

4913 is one

Answer 6

5832 is the other

Answer 7

Yes

Answer 8

I think the third power and the fourth power are the only cases that have
solutions.

Answer 9

Dr, are you going to explain the way of doing it in a more.....'mathematical' way?

Answer 10

The only two numbers are 4913,5832
The solution in AutoIt
For $i=1000 to 9999
$data = StringSplit ($i, "")
$data = $data [1] + $data [2] + $data [3] + $data [4]
$data = $data * $data*$data
If $data = $i Then
$file=FileOpen ("test1.txt", 1)
FileWriteLine ($file, $data)
EndIf
Next

Answer 11

In[171]:=
Clear[x, y, z, w]
n = 9;
U = {};


For[ w = 1, w <= n, w++,
For[ x = 0, x <= n, x++,
For[ y = 0, y <= n, y++,
For[ z = 0, z <= n, z++,


If[1000 w + x + 10 y + 100 z == (w + x + y + z)^3,
U = Append[U, {w, z, y, x}]]]]]]
U

Out[175]= {{4, 9, 1, 3}, {5, 8, 3, 2}}

Answer 12

I will think of a mathematical way to do it. I do not know if there is one.

Answer 13

programming solution .. :D

Answer 14

i was thinking the same way .. :D
i bet nbouscal is better programmer than me :D

Answer 15

Haha probably not I am a very hacky programmer

Answer 16

we are not even allowed to use calculator when doing this type of questions. Let alone programming! (even though I know nothing about programming...)
Thanks doc :)

Answer 17

For this one I just used guess-and-check anyway, no programming