[tex] \displaystyle\\
40)\\
A=\overline{abcd}+\overline{dcba}=\\
=1000a+100b+10c+d + 1000d+100c+10b+a=\\
=1001a + 110b+110c+1001d=\\
1001(a+d)+110(b+c)=\\
11 \times 91(a+d)+11 \times 10(b+c) = \\
=11[91(a+d) + 10(b+c)] ~\vdots~ 11\\
\Longrightarrow~~~11~\Big|~A [/tex]
[tex] 41)
A = \overline{abc}+\overline{bca}+\overline{cab}=\\
100a+10b+c + 100b+10c+a+100c+10a+b=\\
=a(100+10+1)+b(100+10+1)+c(100+10+1)=\\
=111a+111b+111c = 111(a+b+c) = 37\times 3(a+b+c) ~\vdots~37\\
\Longrightarrow~~37~\Big|~A [/tex]
[tex] \displaystyle\\
42)
A=\overline{abc}-\overline{cba}=(100a+10b+c) -(100c+10b+c)=\\
=100a+10b+10c-100c-10b-a =\\
=a(100-1)+b(10-10)+c(1-100)=\\
=99a + 0b -99c=99(a-c)=33\times3(a-c)~\vdots~33\\
\Longrightarrow~~33~\Big|~A [/tex]
