Using Euclids Extended Algorithm:
Calculate x and y in Bézout's Identity
using (3,110)
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 | 110 | Quotient of 3/110 | 0 | |
1 - (0 x 0) | 1 | 0 - (0 x 1) | 0 | Remainder of 3/110 | 3 | Quotient of 110/3 | 36 |
0 - (36 x 1) | -36 | 1 - (36 x 0) | 1 | Remainder of 110/3 | 2 | Quotient of 3/2 | 1 |
1 - (1 x -36) | 37 | 0 - (1 x 1) | -1 | Remainder of 3/2 | 1 | Quotient of 2/1 | 2 |
-36 - (2 x 37) | -110 | 1 - (2 x -1) | 3 | Remainder of 2/1 | 0 | Quotient of 1/0 | 0 |
a = 37 and b = -1
ax + by = gcd(a,b)
3x + 110y = gcd(3