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product of areas AOB,BOC,COD,DOA doesn't end in 1985 Kyiv City MO 7.3

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July 15, 2021
geometryareas

Problem Statement

OO is the point of intersection of the diagonals of the convex quadrilateral ABCDABCD. It is known that the areas of triangles AOB,BOC,CODAOB, BOC, COD and DOADOA are expressed in natural numbers. Prove that the product of these areas cannot end in 19851985.
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