Question

1)Sa se arate ca daca a|a ori b+c si a|a ori c+b, atunci a|bc(cu bara deasupra)+cb(cu bara deasupra).

Answer 1

[tex]Plecam~de~la~faptul~ca~\overline{bc}+\overline{cb}=10b+c+10c+b=11b+11c(asta~e~scrierea~in~baza~10) \\ a~|~a\cdot(b+c)~Cum~a~|~a\Rightarrow a|(b+c)/\cdot11\Rightarrow a~|~11b+11c \\ a~|~a\cdot(c+b)~Cum~a~|~a\Rightarrow a|(c+b)/\cdot11\Rightarrow a~|~11b+11c. \\ Deci~a~|~11\cdot b+11\cdot c\Rightarrow \boxed{a~|~\overline{bc}+\overline{cb}}[/tex]