4. Let a. b e Z. Show that if a E 5 (mod) and b E 3(mod4). then 43+ 617 E 6 (mods). Let 0', t E N be such that d \\ t. Prove that if x,y E Z are such that x E y(mod t), then x E y (mod 0'). Let X,y, u, v E Z and d E N. Prove that ifx E y(mod d) and u E v(mod d), then xu E yv(mod d). Let d E N. Assume that x,y E Z are such that x E y (mod 0'). Prove that x\" E y\" (mod 0') for every n E N