Question

Prove that for all integers a and b. If
a^2(b^2 - 2b) is odd, then a and b are odd​

Answer 1

Answer:

• we have:

a²(b² - 2b) = a²b² - 2a²b

• a²(b² - 2b) is odd but -2a²b is the even number

=> a²b² must be the odd (because an odd number minus an even number equals an odd number)

=> a and b are odd (proven)