Using Euclids Extended Algorithm:
Calculate x and y in Bézout's Identity
using (8,21)
For 2 numbers a and b and divisor d:
ax + by = d
a math | a | b math | b | d math | d | k math | k |
---|---|---|---|---|---|---|---|
Set to 1 | 1 | Set to 0 | 0 | 8 | |||
Set to 0 | 0 | Set to 1 | 1 | 21 | Quotient of 8/21 | 0 | |
1 - (0 x 0) | 1 | 0 - (0 x 1) | 0 | Remainder of 8/21 | 8 | Quotient of 21/8 | 2 |
0 - (2 x 1) | -2 | 1 - (2 x 0) | 1 | Remainder of 21/8 | 5 | Quotient of 8/5 | 1 |
1 - (1 x -2) | 3 | 0 - (1 x 1) | -1 | Remainder of 8/5 | 3 | Quotient of 5/3 | 1 |
-2 - (1 x 3) | -5 | 1 - (1 x -1) | 2 | Remainder of 5/3 | 2 | Quotient of 3/2 | 1 |
3 - (1 x -5) | 8 | -1 - (1 x 2) | -3 | Remainder of 3/2 | 1 | Quotient of 2/1 | 2 |
-5 - (2 x 8) | -21 | 2 - (2 x -3) | 8 | Remainder of 2/1 | 0 | Quotient of 1/0 | 0 |
a = 8 and b = -3
ax + by = gcd(a,b)
8x + 21y = gcd(8