8.1. Compare the numbers: $A=2011 \cdot 20122012 \cdot 201320132013$ and $B=2013 \cdot 20112011 \times$ $\times 201220122012$.
Answer: $A=B$.

$A=2011 \cdot 20122012 \cdot 201320132013=2011 \cdot 2012 \cdot 10001 \cdot 2013 \cdot 100010001$;

$B=2013 \cdot 20112011 \cdot 201220122012=2013 \cdot 2011 \cdot 10001 \cdot 2012 \cdot 100010001$.

Notice that each of the products equals 8146492851648619183716.

+ full justified solution (including direct calculation)

$\mp$ correct answer obtained by factorization, but there is a repetitive computational error (for example, incorrect number of zeros)

- only the answer is provided