Prove or disprove The product of two even integers is divisi

Prove or disprove: The product of two even integers is divisible by 4.

Solution

he following is simply how I restate the problem, saying it exists, that they are integers, and that they are even. I believe the ^ is appropriate here since those are statements? 4|(a·b) and 2|a ^ 2|b : a,bZ Now I introduce n and m. Since I defined a and b as even in the last step, I believe it would be unnecessary here? a n Z : a = 2·n b m Z : b = 2·m I show that 4|[(2·n)(2·m)] relates to 4|(a·b): 4|[(2·n)(2·m)] 4|(4·n·m) 4|(a·b) Therefore; 4|(a·b) [X]