Question

prove that the number(nm(n-m) is even for any integers n and m​

Answer 1

Answer:

Recollect that (Odd number) x (Even number) is always Even.

Also remember that (Even number) - (Even Number) is always Even and that (Odd number) - (Odd number) is always Odd.

Step-by-step explanation:

Let m,n be any two integers, such that m > n.

Case 1: m is even, n is even

mn(m-n) = Even x Even x Even

mn(m-n) is even.

Case 2: m is even, n is odd

mn(m-n) = Even x Odd x Odd

mn(m-n) is even.

Case 3: m is odd, n is even

mn(m-n) = Odd x Even x Odd

mn(m-n) is even.

Case 4: m is odd, n is odd

mn(m-n) = Odd x Odd x Even

mn(m-n) is even.

Thus for any two integers m and n, mn(m-n) is always even.

Hence Proved.

Please mark as Brainliest answer if you found this helpful.