Question

determinati numarul natural xy,x=0,care indeplineste conditia:
a)xy=y²,b)xy=y³​

Answer 1

$\it a)\ \overline{xy}=y^2\ \Rightarrow 10x+y=y^2 \Rightarrow 10x=y^2-y \Rightarrow 10x=y(y-1)_$

$\it 10x\in M_{10}\ \stackrel{(1)}{\Longrightarrow}\ y(y-1)\in M_{10} \Rightarrow y=5\ \ \ \ \ (2)\\ \\ (1), \ (2) \Rightarrow 10x=5\cdot4 \Rightarrow 10x=20 \Rightarrow x=2\\ \\ Deci,\ \ \overline{xy}=25$