HAPPY NEW YEAR $2020$ Remainder Problem I framed a new question just now. What is the Remainder when the number $20^{20}$ is divided by $2020$
My try:
$$\frac{20^{20}}{2020}=\frac{20^{19}}{101}$$
Now Consider:
$$20^{18}=(400)^9=(404-4)^9=101k-2^{18}$$
Now i was trying to find Remainder without calculator or by manual division. 

$20^{19}=100^9\cdot4^9\cdot20=100^9\cdot4^{10}\cdot5=100^9\cdot1024^2\cdot5 \equiv - 14^2\cdot5=-980 \equiv 30 \; (\mod 101)$
