Fermat Last Theorem look-alike

a^n + (p*b)^n = (q*b)^n

Here is the absurd. In fact the number on the right contains in its
decomposition in primes factors the factor q: now for the Euclide's
theorem on the uniqueness of the decomposition in primes factors
also the number on the left has to contain the factor q
which is
not possible because at most two cases should present, both absurd


1) p contains in his decomposition the factor q: this is against the
hypothesis that p and q are primes so this possibility has to be
thrown away

2) b contains in his decomposition the factor q: in this case also the factor
a has to contain, in his decomposition the factor q and thus a and b could
not be primes between them: also this has to be thrown away because
of the previous hypothesis

At the end the negation of the thesis is absurd and therefore it is demonstrated

Ciao
Gianluca Pettinello