Fungrim entry: 99dc4a

Table of

\operatorname{xgcd}\!\left(n, k\right)

for

0 \le n \le 10

and

0 \le k \le 10

$n$ \ $k$	0	1	2	3	4	5	6	7	8	9	10
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:

\left(n, k, \left(d, u, v\right)\right)

such that

\operatorname{xgcd}\!\left(n, k\right) = \left(d, u, v\right)

Definitions:

Fungrim symbol	Notation	Short description
`XGCD`	$\operatorname{xgcd}\!\left(a, b\right)$	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)))))

Topics using this entry

Greatest common divisor