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Question Number 155206 by mathdanisur last updated on 26/Sep/21

$$\mathrm{Determine}\mathrm{all}\mathrm{positive}\mathrm{integers}$$$$\mathrm{a};\mathrm{b};\mathrm{c};\mathrm{d};\mathrm{x};\mathrm{y};\mathrm{z};\mathrm{t}\mathrm{and}\mathrm{a}\ne \mathrm{b}\ne \mathrm{c}\ne \mathrm{d}$$$$\mathrm{which}\mathrm{satisfy}\mathrm{a}+\mathrm{b}+\mathrm{c}=\mathrm{td};$$$$\mathrm{b}+\mathrm{c}+\mathrm{d}=\mathrm{xa};\mathrm{c}+\mathrm{d}+\mathrm{a}=\mathrm{yb};\mathrm{d}+\mathrm{a}+\mathrm{b}=\mathrm{zc}$$

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