Question

Problemele incercuite.Va rog!!!!

Answer 1

 

[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]