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