The discussion revolves around proving that there are no natural numbers x and y that satisfy the equation y^5 + 1 = (x^7 - 1)/(x - 1). Participants are exploring various mathematical approaches and reasoning related to this statement.
The discussion is active, with participants providing insights and questioning each other's reasoning. Some participants have suggested potential paths forward, while others express uncertainty about specific steps or theorems being referenced.
There are mentions of specific cases regarding the nature of x and c being fifth powers, and the implications of their coprimality. Participants are also considering the constraints of positive integer values in their reasoning.
But then C and x wouldn't be coprime they would have common factor b.Faiq said: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