Show no natural numbers satisfy y^5 + 1 = (x^7-1)/(x-1)

[Delta2]

I don't think its necessary for both to be a fifth power consider this
y5 = (ab)5 = a5.b5
C = a5.b
x = b4
y5 = cx = (a5.b)(b4) = a5.b5 =(ab)5

But then C and x wouldn't be coprime they would have common factor b.

 

[Faiq]

Oh yeah right thanks

 

[Delta2]

Btw you are right about case 1 and 3 we just omitted them because they kind of intuitively obvious that they lead to contradiction.

 

[Faiq]

Thank you very much for the help