Using Euclids Extended Algorithm:
Calculate x and y in Bézout's Identity
using (3,4)
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 | 3 | |||
Set to 0 | 0 | Set to 1 | 1 | 4 | Quotient of 3/4 | 0 | |
1 - (0 x 0) | 1 | 0 - (0 x 1) | 0 | Remainder of 3/4 | 3 | Quotient of 4/3 | 1 |
0 - (1 x 1) | -1 | 1 - (1 x 0) | 1 | Remainder of 4/3 | 1 | Quotient of 3/1 | 3 |
1 - (3 x -1) | 4 | 0 - (3 x 1) | -3 | Remainder of 3/1 | 0 | Quotient of 1/0 | 0 |
a = -1 and b = 1
ax + by = gcd(a,b)
3x + 4y = gcd(3