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Fungrim entry: 99dc4a

Table of xgcd ⁣(n,k)\operatorname{xgcd}\!\left(n, k\right) for 0n100 \le n \le 10 and 0k100 \le k \le 10
nn \ kk 012345678910
0(0, 0, 0)(1, 0, 1)(2, 0, 1)(3, 0, 1)(4, 0, 1)(5, 0, 1)(6, 0, 1)(7, 0, 1)(8, 0, 1)(9, 0, 1)(10, 0, 1)
1(1, 1, 0)(1, 0, 1)(1, 1, 0)(1, 1, 0)(1, 1, 0)(1, 1, 0)(1, 1, 0)(1, 1, 0)(1, 1, 0)(1, 1, 0)(1, 1, 0)
2(2, 1, 0)(1, 0, 1)(2, 0, 1)(1, -1, 1)(2, 1, 0)(1, -2, 1)(2, 1, 0)(1, -3, 1)(2, 1, 0)(1, -4, 1)(2, 1, 0)
3(3, 1, 0)(1, 0, 1)(1, 1, -1)(3, 0, 1)(1, -1, 1)(1, 2, -1)(3, 1, 0)(1, -2, 1)(1, 3, -1)(3, 1, 0)(1, -3, 1)
4(4, 1, 0)(1, 0, 1)(2, 0, 1)(1, 1, -1)(4, 0, 1)(1, -1, 1)(2, -1, 1)(1, 2, -1)(4, 1, 0)(1, -2, 1)(2, -2, 1)
5(5, 1, 0)(1, 0, 1)(1, 1, -2)(1, -1, 2)(1, 1, -1)(5, 0, 1)(1, -1, 1)(1, 3, -2)(1, -3, 2)(1, 2, -1)(5, 1, 0)
6(6, 1, 0)(1, 0, 1)(2, 0, 1)(3, 0, 1)(2, 1, -1)(1, 1, -1)(6, 0, 1)(1, -1, 1)(2, -1, 1)(3, -1, 1)(2, 2, -1)
7(7, 1, 0)(1, 0, 1)(1, 1, -3)(1, 1, -2)(1, -1, 2)(1, -2, 3)(1, 1, -1)(7, 0, 1)(1, -1, 1)(1, 4, -3)(1, 3, -2)
8(8, 1, 0)(1, 0, 1)(2, 0, 1)(1, -1, 3)(4, 0, 1)(1, 2, -3)(2, 1, -1)(1, 1, -1)(8, 0, 1)(1, -1, 1)(2, -1, 1)
9(9, 1, 0)(1, 0, 1)(1, 1, -4)(3, 0, 1)(1, 1, -2)(1, -1, 2)(3, 1, -1)(1, -3, 4)(1, 1, -1)(9, 0, 1)(1, -1, 1)
10(10, 1, 0)(1, 0, 1)(2, 0, 1)(1, 1, -3)(2, 1, -2)(5, 0, 1)(2, -1, 2)(1, -2, 3)(2, 1, -1)(1, 1, -1)(10, 0, 1)
Table data: (n,k,(d,u,v))\left(n, k, \left(d, u, v\right)\right) such that xgcd ⁣(n,k)=(d,u,v)\operatorname{xgcd}\!\left(n, k\right) = \left(d, u, v\right)
Definitions:
Fungrim symbol Notation Short description
XGCDxgcd ⁣(a,b)\operatorname{xgcd}\!\left(a, b\right) Extended greatest common divisor
Source code for this entry:
Entry(ID("99dc4a"),
    Description("Table of", XGCD(n, k), "for", LessEqual(0, n, 10), "and", LessEqual(0, k, 10)),
    Table(TableRelation(Tuple(n, k, Tuple(d, u, v)), Equal(XGCD(n, k), Tuple(d, u, v))), TableHeadings(Description(n, "\", k), 0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10), TableColumnHeadings(0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10), List(Tuple(Tuple(0, 0, 0), Tuple(1, 0, 1), Tuple(2, 0, 1), Tuple(3, 0, 1), Tuple(4, 0, 1), Tuple(5, 0, 1), Tuple(6, 0, 1), Tuple(7, 0, 1), Tuple(8, 0, 1), Tuple(9, 0, 1), Tuple(10, 0, 1)), Tuple(Tuple(1, 1, 0), Tuple(1, 0, 1), Tuple(1, 1, 0), Tuple(1, 1, 0), Tuple(1, 1, 0), Tuple(1, 1, 0), Tuple(1, 1, 0), Tuple(1, 1, 0), Tuple(1, 1, 0), Tuple(1, 1, 0), Tuple(1, 1, 0)), Tuple(Tuple(2, 1, 0), Tuple(1, 0, 1), Tuple(2, 0, 1), Tuple(1, -1, 1), Tuple(2, 1, 0), Tuple(1, -2, 1), Tuple(2, 1, 0), Tuple(1, -3, 1), Tuple(2, 1, 0), Tuple(1, -4, 1), Tuple(2, 1, 0)), Tuple(Tuple(3, 1, 0), Tuple(1, 0, 1), Tuple(1, 1, -1), Tuple(3, 0, 1), Tuple(1, -1, 1), Tuple(1, 2, -1), Tuple(3, 1, 0), Tuple(1, -2, 1), Tuple(1, 3, -1), Tuple(3, 1, 0), Tuple(1, -3, 1)), Tuple(Tuple(4, 1, 0), Tuple(1, 0, 1), Tuple(2, 0, 1), Tuple(1, 1, -1), Tuple(4, 0, 1), Tuple(1, -1, 1), Tuple(2, -1, 1), Tuple(1, 2, -1), Tuple(4, 1, 0), Tuple(1, -2, 1), Tuple(2, -2, 1)), Tuple(Tuple(5, 1, 0), Tuple(1, 0, 1), Tuple(1, 1, -2), Tuple(1, -1, 2), Tuple(1, 1, -1), Tuple(5, 0, 1), Tuple(1, -1, 1), Tuple(1, 3, -2), Tuple(1, -3, 2), Tuple(1, 2, -1), Tuple(5, 1, 0)), Tuple(Tuple(6, 1, 0), Tuple(1, 0, 1), Tuple(2, 0, 1), Tuple(3, 0, 1), Tuple(2, 1, -1), Tuple(1, 1, -1), Tuple(6, 0, 1), Tuple(1, -1, 1), Tuple(2, -1, 1), Tuple(3, -1, 1), Tuple(2, 2, -1)), Tuple(Tuple(7, 1, 0), Tuple(1, 0, 1), Tuple(1, 1, -3), Tuple(1, 1, -2), Tuple(1, -1, 2), Tuple(1, -2, 3), Tuple(1, 1, -1), Tuple(7, 0, 1), Tuple(1, -1, 1), Tuple(1, 4, -3), Tuple(1, 3, -2)), Tuple(Tuple(8, 1, 0), Tuple(1, 0, 1), Tuple(2, 0, 1), Tuple(1, -1, 3), Tuple(4, 0, 1), Tuple(1, 2, -3), Tuple(2, 1, -1), Tuple(1, 1, -1), Tuple(8, 0, 1), Tuple(1, -1, 1), Tuple(2, -1, 1)), Tuple(Tuple(9, 1, 0), Tuple(1, 0, 1), Tuple(1, 1, -4), Tuple(3, 0, 1), Tuple(1, 1, -2), Tuple(1, -1, 2), Tuple(3, 1, -1), Tuple(1, -3, 4), Tuple(1, 1, -1), Tuple(9, 0, 1), Tuple(1, -1, 1)), Tuple(Tuple(10, 1, 0), Tuple(1, 0, 1), Tuple(2, 0, 1), Tuple(1, 1, -3), Tuple(2, 1, -2), Tuple(5, 0, 1), Tuple(2, -1, 2), Tuple(1, -2, 3), Tuple(2, 1, -1), Tuple(1, 1, -1), Tuple(10, 0, 1)))))

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Copyright (C) Fredrik Johansson and contributors. Fungrim is provided under the MIT license. The source code is on GitHub.

2019-08-19 14:38:23.809000 UTC