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

Let a,b and c be positive integers such  that ab+1∣bc+1 and bc+1∣ca+1.  Show that ab+1 is the sum of two  squares.

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

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