Question

For any even integer prove that
48 | a(a+ 20)
​

Answer 1

order by

up vote

7

down vote

accepted

Since n is even, we can write n=2k for some integer k.

Hint:

n(n2+20)=2k((2k)2+20)=2k(4k2+20)=8k(k2+5)

Hence, 8 is a factor.

Note further that one of k or k2+5 must be even, and hence divisible by 2. Why?

So now we know that 8⋅2=16 is a factor.