19. If m and n are two positive integers and (m,n) is an even number, by which of the following (mt -n') is always divisible? (1) 2 (2) 8 (3) 4 (4) 12
Solution19. (3) Since, (m-n) is an even number. therefore m and n both are either even or odd. And then (m+ n) is even. Now, (m2-n2)=(m+ n)x(m-n) Which is the multiplication of two even numbers and therefore always be divisible by 4.