Determine all pairs \((x, y)\) of integers satisfying the equation:\[1+2^{x}+2^{2x+1}=y^{2}\] If your answers are \[(x_{1};y_{1}),(x_{2};y_{2}),\cdot\cdot\cdot,(x_{n};y_{n})\] type it as \[y_{1}^{x_{1}}+y_{2}^{x_{2}}+ \cdot\cdot\cdot +y_{n}^{x_{n}}\]

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