Question

Arătati ca:
(Abc+bca+cab) se divide la 37
Determinări nr. 2x7y care se divide cu 2 si cu 9

Answer 1

(1)... [tex] \overline{abc}+\overline{bca}+\overline{cab}=\\ =100a+10b+c+100b+10c+a+100c+10a+b=\\ =11cdot(a+b+c)\;\vdots37\;\;pentru\;ca\;111\vdots37\;;\\ [/tex]
(2)... [tex]\overline{2x7y}\,\vdots\,(2\cdot9)\;\;daca y=\{0;2;4;6;8\} si\\ 2+x+7+0=M_9 \;adica\;x=\{9\} \rightarrow\;\;\fbox{2970}\\ 2+x+7+2=M_9\;adica\;x=\{7\}\rightarrow\;\;\fbox{2772}\\ 2+x+7+4=M_9\;adica\;x=\{5\}\rightarrow\;\;\fbox{2574}\\ 2+x+7+6=M_9\;adica\;x=\{3\}\rightarrow\;\;\fbox{2376}\\ 2+x+7+8=M_9\;adica\;x=\{10\}\;dar \,nu \,ne \,convine[/tex]