Show that 9453(6824)$\equiv$6782(5675341)$\equiv$2 (mod 5)

Question

Show that 9453(6824)$\equiv$6782(5675341)$\equiv$2 (mod 5)

I am very new to modular arithmetic and I am not entirely sure what this question is asking me to do, or how you would go about showing what it is looking for. I apologise if this is very simple, but I am looking for some clarification on what this actually means. Thanks.

Answer 1

Hint: $a\equiv r$ (mod $p$), where $r$ is the remainder when $a$ is divided by $p$.

What are the remainders when $9453, 6824, 6782$ and $5675341$ are divided by $5$?

Answer 2

Hint. It is relatively easy to reduce numbers in decimal form modulo $5.$ Just expand out and note that any positive power of $10$ vanishes modulo $5.$ Thus, the residues are just the residues of the units digits, which are easy to do. Can you now proceed?