`C_1, C_2 = (a, b)`

Enter a value for all fields

The Bézout Coefficients equation returns two coefficients a and b that satisfy the equation ax + by = gcd(a, b).

INSTRUCTIONS: Enter the following

• (a) First number (smaller)
• (b) Second number (greater)

Bézout Coefficients (C₁, C₂): The equation returns the Bézout Coefficients for the numbers a and b

Example

• a = 14
• b = 123

121 = 3 x 36 + 13

36 = 2 x 13 + 10

13 = 1 x 10 + 3

10 = 3 x 3 + 1  

3 = 3 x 1 + 0

 

1 = 10 - 3(3) ––> 1 = 10 - 3[(13-1(10)] ––> 1 = 10 - 3(13) + 3(10) ––> 1 = -3(13 + 4(10)

1 = -3(13) + 4(10)  ––> 1 = 4(10) - 3[36 - 2(13)] ––> 1 = -3(13) + 4(36) - 8(13) ––> 1 = 4(36) - 11(13)

1 = 4(36) - 11(13) ––> 1 = 4(36) - 11[121 - 3(36)] ––> 1 = 4(36) - 11(121) + 33(36) ––> 1 = -11(121) + 37(36)

 

C₁ = 37

C₂ = -11