Question

Sa se arate ca abc(in baza 10)+bca(in baza 10) se divide cu 112, stiind ca a=10b+c

Answer 1

abc+bca=100*a+10*b+c+100*b+10*c+a=101*a + 110*b+11*c
a=10b+c

=101 * (10b+c) + 110*b+ 11*c=
=1010*b+101*c + 110*b + 11*c=
=1120*b+112*c=112* (10*b+c). Rezulta ca 112 divide suma abc+bca,

Spor la invatat!