I read in a book about Fermats last theorem that it has been proved that "if there are solutions to the equation a^n+b^n=c^n, then there are only a finite number of them". I searched this up and found this article:

How can this be?
Suppose [tex]a_0, b_0[/tex] and [tex]c_0[/tex] are solutions to the equation [tex]a^n+b^n=c^n[/tex] for a specified n, i.e [tex]a_0^n+b_0^n=c_0^n[/tex]. But by multiplying by [tex]k^n[/tex] where k is a natural number larger than 1 yields [tex](a_0k)^n+(b_0k)^n=(c_0k)^n[/tex] which is a different solution. This is true for all values of k larger than 1, so I cannot see how the theorem is true.