Question

Impartind 2 numere naturale unul la celalalt se obtine catul 3 si un rest. Impartind acelasi numar la trei se obtine acelasi rest. Aflati numerele stiind ca suma lor este 158.

Answer 1

a:b=3+r => a=3b+r a:3=c+r => r<3 a+b=158 3b+r+b=158 4b=158-r Daca r=0 => 4b=158 (Fals) Daca r=1 => 4b=157 (Fals) Daca r=2 => 4b=156 => b=156:4=39 Daca r=3 => 4b=155 (Fals) a+39=158 => a=158-39=119 Proba 119:39=3 rest 2 (A) 119:3=39 rest 2 (A)