Star equation

Write digits instead of stars so that the sum of the written digits is odd and is true equality:

42 · ∗8 = 2 ∗∗∗

Correct answer:

b₁ =  48
b₂ =  68
c₁ =  2016
c₂ =  2856

Step-by-step explanation:

$$\begin{gathered} a=42 \\ {s}_1=a\cdot 18=42\cdot 18=756 \\ {s}_2=a\cdot 28=42\cdot 28=1176 \\ {s}_3=a\cdot 38=42\cdot 38=1596 \\ {s}_4=a\cdot 48=42\cdot 48=2016 \\ {s}_5=a\cdot 58=42\cdot 58=2436 \\ {s}_6=a\cdot 68=42\cdot 68=2856 \\ {s}_7=a\cdot 78=42\cdot 78=3276 \\ 2000<=s<=2999 \\ S=2016,2436,2856 \\ {x}_1=4+0+1+6=11 \\ {x}_2=5+4+3+6=18 \\ {x}_3=6+8+5+6=25 \\ {x}_1=nepar \\ {b}_1=48=48 \end{gathered}$$

$b_2=68=68$

$c_1=a\cdot b_1=42\cdot 48=2016$

$c_2=a\cdot b_2=42\cdot 68=2856$

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