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A201006
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The Isis problem : Array a(i,j) (by antidiagonals) of differences between area and perimeter of rectangle with sides (i,j).
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0
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-3, -4, -4, -5, -4, -5, -6, -4, -4, -6, -7, -4, -3, -4, -7, -8, -4, -2, -2, -4, -8, -9, -4, -1, 0, -1, -4, -9, -10, -4, 0, 2, 2, 0, -4, -10, -11, -4, 1, 4, 5, 4, 1, -4, -11, -12, -4, 2, 6, 8, 8, 6, 2, -4, -12, -13, -4, 3, 8, 11, 12, 11, 8, 3, -4, -13, -14, -4, 4, 10, 14, 16, 16, 14, 10, 4, -4, -14, -15, -4, 5, 12, 17, 20, 21, 20, 17, 12, 5, -4, -15, -16, -4, 6, 14, 20, 24, 26, 26, 24, 20, 14, 6, -4, -16
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OFFSET
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0,1
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COMMENTS
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Quotation from the reference: "Which rectangles with integer sides (in some unit) have the property that the area and the perimeter are (numerically) equal? It is not difficult to prove that there are precisely two rectangles with integer sides (in some unit of length) that have the property that the area and perimeter are numerically equal, namely 4 × 4 and 3 × 6".
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REFERENCES
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Greer, Brian & Bock, Dirk De & Dooren, Wim Van, The ISIS Problem and Pre-Service Teachers’ Ideas about Proof, in Proceedings of the ICMI Study 19 conference: Proof and Proving in Mathematics Education 1-184
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LINKS
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MATHEMATICA
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a[i_, j_] := i*j - 2i - 2j; Table[a[i - j + 1, j], {i, 1, 14}, {j, 1, i}] // Flatten
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CROSSREFS
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KEYWORD
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AUTHOR
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STATUS
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approved
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