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Question Number 110775 by Aina Samuel Temidayo last updated on 30/Aug/20

$$\mathrm{Let}\mathrm{a},\mathrm{b}\mathrm{and}\mathrm{c}\mathrm{be}\mathrm{positive}\mathrm{integers}\mathrm{such}$$$$\mathrm{that}\mathrm{ab}+1\mid \mathrm{bc}+1\mathrm{and}\mathrm{bc}+1\mid \mathrm{ca}+1.$$$$\mathrm{Show}\mathrm{that}\mathrm{ab}+1\mathrm{is}\mathrm{the}\mathrm{sum}\mathrm{of}\mathrm{two}$$$$\mathrm{squares}.$$

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