Question

8. Arătați că:

a) E = ($\frac{}{abc}$ + $\frac{}{bca}$ + $\frac{}{cab}$) divizibil cu 37.

class: VI.

Answer 1

$\text{Se foloseste descompunerea in baza 10:}\\E=\overline{abc}+\overline{bca}+\overline{cab}\\E=100a+10b+c+100b+10c+a+100c+10a+b\\E=111a+111b+111c\\E=111(a+b+c)\\E=37\cdot 3\cdot (a+b+c) \Rightarrow E~\vdots~ 37$