Excuse me that message got sent accidentally, It was supposed to be longer
I was asked to prove that if p_1, ..., p_t are different primes then these are linear independent given that the coefficients are rational. Now, I know that if for every x in Q, there exists a sequence of primes n_p such that
x= sign(x) \product p^{n_p}. I know I can use this here, yet I am not sure how to start the proof.