Prove that the language A = {(p,q) | p and q are equivalent programs} is uncomputable.
Hint. The language B = {p | p loops forever on every input} is uncomputable. Do a reduction to show that A is uncomputable.
Hint. Do a reduction from the halting proglem. You will want to design a program that ignores its input, so that it will do the same thing on every input.