$$\sum\limits_{r=1}^{20}\left(r^{2}+1\right)(r !)$$ is equal to

The remainder when $$7^{2022}+3^{2022}$$ is divided by 5 is :

The remainder when $$(2021)^{2022}+(2022)^{2021}$$ is divided by 7 is

$$\sum\limits_{\matrix{ {i,j = 0} \cr {i \ne j} \cr } }^n {{}^n{C_i}\,{}^n{C_j}} $$ is equal to