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2020 Australian Mathematical OlympiadSolution 8 (Dan Mathews) First Note That √ Ab =(a+b)/2−1 Must Be An Integer Or Half Integer; But The Square Root Of An Integer Is Never A Half Integer, Hence Ab Is A Perfect Square. If A,b Have A Prime Factor P>2 In Common, Then It Must Divide √ Ab And (a + B)/2, But Not 1, A Contradiction.So The Only Possible Common Prime 1th, 2024AUSTRALIAN MATHEMATICAL OLYMPIAD 2018A USTR A LI A N M A THE MA TIC A L O LY M PI A D C OMM ITTEE A DEP A RT M ENT O F THE A USTR A LI A N MA THE MA TICS TRUST Solution 4 (Daniel Mathews) First, We Claim That AE Is The Angle Bisector Of AC And AG.To See This, Note That CEG Is Isosceles, With ∠ECG = ∠EGC; And As ACEG Is Cyclic, Then ∠EAG = ∠EAC. Second, We Si 1th, 2024AUSTRALIAN MATHEMATICAL OLYMPIAD 2017 2017 …Official Sponsor Of The Olympiad Program. AUSTRALIAN MATHEMATICAL OLYMPIAD 2017 DAY 1 Tuesday, 14 February 2017 Time Allowed: 4 Hours No Calculators Are To Be Used. Each Question Is Worth Seven Points. 1. For Which Integers N ≥ 2 Is 2th, 2024.
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