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Question Number 25723 by Joel578 last updated on 13/Dec/17
Given a_1 , a_2 , ..., a_n  are non−negative  integers and satisfy  (1/2^a_1  ) + (1/2^a_2  ) + ... + (1/2^a_n  ) = (1/3^a_1  ) + (2/3^a_2  ) + ... + (n/3^a_n  ) = 1   If n is positive integer, find all possible solution  of n
$$\mathrm{Given}\:{a}_{\mathrm{1}} ,\:{a}_{\mathrm{2}} ,\:…,\:{a}_{{n}} \:\mathrm{are}\:\mathrm{non}−\mathrm{negative} \\ $$$$\mathrm{integers}\:\mathrm{and}\:\mathrm{satisfy} \\ $$$$\frac{\mathrm{1}}{\mathrm{2}^{{a}_{\mathrm{1}} } }\:+\:\frac{\mathrm{1}}{\mathrm{2}^{{a}_{\mathrm{2}} } }\:+\:…\:+\:\frac{\mathrm{1}}{\mathrm{2}^{{a}_{{n}} } }\:=\:\frac{\mathrm{1}}{\mathrm{3}^{{a}_{\mathrm{1}} } }\:+\:\frac{\mathrm{2}}{\mathrm{3}^{{a}_{\mathrm{2}} } }\:+\:…\:+\:\frac{{n}}{\mathrm{3}^{{a}_{{n}} } }\:=\:\mathrm{1}\: \\ $$$$\mathrm{If}\:{n}\:\mathrm{is}\:\mathrm{positive}\:\mathrm{integer},\:\mathrm{find}\:\mathrm{all}\:\mathrm{possible}\:\mathrm{solution} \\ $$$$\mathrm{of}\:{n}\: \\ $$

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