Prove that if n ∈ N is odd then 2019n 2 − 2020n + 2021 is even.

Question

Prove that if n ∈ N is odd then 2019n 2 − 2020n + 2021 is even.

Answer 1

Does n 2 mean n ^ 2 ?

2019 x n x n = odd x odd x odd = odd

2020 x n = even x odd = even

Thus, we have

Odd - even + odd = odd + odd = even