Question

"The product of any two even integers is a multiple of 4."

This is what I have so far:
let n, m be even integers and let d be a integer that isdivisible by 4.
n=2k.
m=2l.
d=4p.
such that k,l,p exists in Z (integers).
n • m = d
2k • 2l = 4p
2(k•l)=4p.

Answer 1

The product of any two even integers is indeed a multiple of 4 because an even integer is defined as 2 times another integer. When two even integers are multiplied together, the product includes a factor of 4 (since 2 • 2 equals 4), ensuring that the product is divisible by 4.

Step-by-step explanation:

When analyzing the statement “The product of any two even integers is a multiple of 4,” we must consider the basic properties of even integers. An even integer is defined as any integer that can be expressed as 2 times another integer, such as n = 2k and m = 2l, where k and l are integers. Multiplying these two even integers together we get:

n • m = (2k) • (2l) = 4(kl),

where kl is also an integer since it is a product of two integers. Here, we see that n • m can indeed be rewritten as 4 times an integer p (where p is equal to kl), confirming that n • m is a multiple of 4 as initially stated. This is because the product contains a factor of 4 (2 • 2), which guarantees that the entire product is divisible by 4.