to prove that there is no rational numbers whose square is equal to 2, my book states that:
lets use the fact that a prime factor of a square number occurs an even number of times. this p^2 = 2q^2. on the LHS, the prime factor 2 must occur an even number of times while RHS, 2 will occur an odd number of times.
thus this is a contradiction to the fact that prime factorization of a number is unique.
hi! could someone explain to me what does it mean to the sentence in bold and why it leads to the proposition being true?