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A298860
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Primitive cyclic quadrilaterals with integer area.
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3
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1, 3, 6, 8, 18, 12, 1, 5, 5, 7, 18, 16, 1, 2, 8, 9, 20, 12, 1, 5, 5, 9, 20, 15, 1, 4, 7, 8, 20, 18, 2, 5, 5, 8, 20, 20, 2, 5, 5, 10, 22, 18, 3, 5, 5, 9, 22, 24, 2, 4, 7, 11, 24, 20, 3, 5, 5, 11, 24, 21, 4, 5, 5, 10, 24, 28, 2, 6, 7, 9, 24, 30, 4, 5, 5, 12, 26, 24, 3, 4, 8, 11, 26, 30, 4, 5, 7, 10, 26, 36, 2, 5, 10, 11, 28, 36, 1, 7, 8, 14, 30, 28, 1, 8, 9, 12, 30, 42
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OFFSET
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1,2
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COMMENTS
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Entries are listed as sextuples: (a,b,c,d), Perimeter, Area. They are ordered first by perimeter, second by area, third by a, then b, then c, then d. Rectangles and kites with two right angles are not listed; thus a < b <= c <= d. By "primitive" we mean (a,b,c,d) is not a multiple of any earlier quadruple.
We observe that the number of odd integers in any quadruple is always an even number.
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LINKS
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EXAMPLE
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The first row of the table gives sidelengths (a,b,c,d)=(1,3,6,8) with perimeter=18 and area=12. Thus:
a b c d Perim Area
= = = == ===== ====
1 3 6 8 18 12
1 5 5 7 18 16
1 2 8 9 20 12
1 5 5 9 20 15
1 4 7 8 20 18
2 5 5 8 20 20
2 5 5 10 22 18
3 5 5 9 22 24
2 4 7 11 24 20
3 5 5 11 24 21
4 5 5 10 24 28
etc.
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CROSSREFS
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Cf. A298907, A297790, A210250, A230136, A131020, A218431, A219225, A233315, A242778, A273691, A273890.
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KEYWORD
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nonn,tabf
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AUTHOR
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STATUS
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approved
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