let $k = 1^1+2^2+...+2021^{2021}+2022^{2022}$
what is the last digit of $k$?
I've tried isolating a couple of terms, more specifically the ones that shared the same last digit, as such I've noted $10$ sums from $1$ to $10$:
$$S_1=1^1+11^{11}+..+2021^{2021}$$
$$S_2=2^2+12^{12}+...+2022^{2022}$$ and so on
From here I've basically tried to say the last digit of these sums would be equal with the following:
$$U(S_1) = 1^1 + 1^{11} + ... + 1^{2021}$$
$$U(S_2) = 2^2 + 2^{12} + ... + 2^{2022}$$
$$U(S_3) = 3^3 + 3^{13} + ... + 3^{2013}$$
Thus I'm not sure how to proceed from here, nor if my reasoning is even remotely correct.
