number theory – Show that 2020 divides \$pleft( n right)\$ for every integer \$n\$

Consider:
$$pleft( n right)=800n+400{{n}^{2}}+400{{n}^{4}}+200{{n}^{5}}+100{{n}^{10}}+100{{n}^{20}}+8{{n}^{101}}+4{{n}^{202}}+4{{n}^{404}}+2{{n}^{505}}+{{n}^{1010}}+{{n}^{2020}}$$
Show that: $$2020$$ divides $$pleft( n right)$$ for every positive integer $$n$$?

Work: the statement is indeed true for $$n=1,2..100$$ , of course using a computer!!