Răspuns:
2430 si 2835
Explicație pas cu pas:
[tex] 45 \mid \overline{2a3b}\\ \\ \implies 9 \mid \overline {2a3b} \implies 2+a+3+b = 9k_1 \implies a+b = 9k - 5\implies a+b \in \{4; 13\}\\ \\ \implies 5 \mid \overline{2a3b} \implies b \in \{0, 5\}\\ \\ b = 0, a+b = 4\implies a+0 = 4\implies a = 4\\ \\ b = 0, a+b = 13\implies a+0 = 13 \implies a = 13 \nless 10\\ \\ b = 5, a+b = 4\implies a+5 = 4\implies a = -1 \notin \mathbb{N}\\ b = 5, a+b = 13\implies a+5 = 13\implies a = 8\\ \\ S = \{(4,0); (8,5)\}\\ \\ \text{Numerele sunt:}\\ \\ \text{2430 si 2835}[/tex]
