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A348143
Areas of integer-sided cyclic quadrilaterals whose area equals their perimeter.
1
16, 18, 20, 30
OFFSET
1,1
COMMENTS
There are no further terms. Note that without the condition "integer-sided" there are other solutions, such as (1, 17/2, 17/2, 16) which has perimeter and area 34.
EXAMPLE
The areas or perimeters 16, 18, 20, 30 pertain respectively to cyclic quadrilaterals with sides (4, 4, 4, 4), (3, 3, 6, 6), (2, 5, 5, 8), (5, 5, 6, 14).
MATHEMATICA
lst={}; Do[s=(a+b+c+d)/2; If[s>a, (K=Sqrt[(s-a)(s-b)(s-c)(s-d)]; If[IntegerQ[K]&&K==2s, AppendTo[lst, Sort@{a, b, c, d}]])], {a, 1, 15}, {b, 1, a}, {c, 1, b}, {d, 1, c}]; lst
CROSSREFS
Cf. A098030, A290451. First four terms of A161874.
Sequence in context: A273543 A274127 A328736 * A161874 A095953 A084800
KEYWORD
fini,full,nonn
AUTHOR
Frank M Jackson, Oct 02 2021
STATUS
approved