Question
the only perfect number of the form (x to the power of n) + (y to the power of n)
Perfect numbers have the form
2<sup>kâ1</sup>(2<sup>k</sup> â 1)
The first few perfect number are 6,28,496 and 8,128.
Does n have to be something other than 1 in your question?
I can see 28 = 1<sup>3</sup> + 3<sup>3</sup>
but I'm not sure it's the only number that can be written like this, at least I've never seen a proof or conjecture on this.
sarah, do you go to OCHS?
Perfect numbers have the form
2<sup>kâ1</sup>(2<sup>k</sup> â 1)
The first few perfect number are 6,28,496 and 8,128.
Does n have to be something other than 1 in your question?
I can see 28 = 1<sup>3</sup> + 3<sup>3</sup>
but I'm not sure it's the only number that can be written like this, at least I've never seen a proof or conjecture on this.
sarah, do you go to OCHS?