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a+1|b^2+c^2 , b+1|c^2+a^2 , c+1|a^2+b^2

Source: 2006 VMEO III Shortlist SL N6 Vietnamese Mathematics e - Olympiad https://artofproblemsolving.com/community/c2461015_vmeo__viet

October 5, 2021
number theorydivides

Problem Statement

Find all sets of natural numbers (a,b,c)(a, b, c) such that a+1∣b2+c2  ,b+1∣c2+a2  ,c+1∣a2+b2.a+1|b^2+c^2\,\, , b+1|c^2+a^2\,\,, c+1|a^2+b^2.
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