Number theory a divides b if there exists cs. t b= ac (denoted by ab) properties for all a, b,cE Z -aa -if a b and blc, then alc if a b and ac, then al(bx+cy) for all y E Z if ab and bla, then a=±b 1818 Number theory • a divides b if there exists c s.t. b = ac (denoted by a|b) • properties for all a,b,c  Z – a|a – if a|b and b|c, then a|c – if a|b and a|c, then a|(bx+cy) for all x,y  Z – if a|b and b|a, then a = b