I can show the following proofs for specific examples, but can't do the actual proof itself. Any way of starting would be great. I thought about induction, but I can't understand how that would work.

Show that the product of 2 primes that are both congruent 3 (mod 4) is congruent 1 (mod 4)

Show that the product of any no. of primes that are congruent 1 (mod 4) is congruent 1 (mod 4)

Show that the product of any no. of odd primes is congruent 1 (mod 4), unless an odd no. of the primes are congruent 3 (mod 4)

thanks