[tex]\it 2x-3y=4 \Rightarrow x=\dfrac{4+3y}{2} \Rightarrow x = \dfrac{4+2y+y}{2} \Rightarrow x = 2+y+\dfrac{y}{2} \ \ \ \ (*)
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x, \ y \in \mathbb{N} \stackrel{(*)}{\Longrightarrow} \dfrac{y}{2} \in\mathbb{N} \Rightarrow y=2k,\ \ k\in \mathbb{N}
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y=2k \stackrel{(*)}{\Longrightarrow} x = 2+2k+k \Rightarrow x = 3k+2, k\in \mathbb{N} [/tex]
[tex]\it Pentru\ \ x = 3k+2,\ \ y=2k, \ avem:
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(x-2)(y+2) = (3k+2-2)(2k+2)= 3k\cdot2(k+1) =6k(k+1) \Rightarrow
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\Rightarrow 6\vdots (x-2)(y+2) [/tex]
