Răspuns :
[tex]
\overline{abc}+\overline{bca}+\overline{cab}=[/tex]
[tex]=100a+10b+c+100b+10c+a+100c+10a+b=[/tex]
[tex]=111a+111b+111c=[/tex]
[tex]=111(a+b+c)=[/tex]
[tex]=37*3(a+b+c)[/tex]
=>[tex](
\overline{abc}+\overline{bca}+\overline{cab})[/tex]⋮37
\overline{abc}+\overline{bca}+\overline{cab}=[/tex]
[tex]=100a+10b+c+100b+10c+a+100c+10a+b=[/tex]
[tex]=111a+111b+111c=[/tex]
[tex]=111(a+b+c)=[/tex]
[tex]=37*3(a+b+c)[/tex]
=>[tex](
\overline{abc}+\overline{bca}+\overline{cab})[/tex]⋮37