Originally Posted by

**sir nerdalot**

For example... 51 and 44 are relatively prime.

**Repeated use of the division identity leads to:**

51 = 44 x 1 + 7

44 = 7 x 6 + 2

7 = 3 x 2 + 1

Reversing these steps leads to:

1 = 7 - 3 x 2

= 7 - 3(44 - 7 x 6)

= 19 x 7 - 3 x 44

= 19(51 - 44 x 1) - 3 x 44

= 19 x 51 - 22 x 44

question...

a) use this method to find integers 'a' and 'b' such that 87a + 19b = 1.

b) using the method, find the polynomials, A(x) and B(x) such that:

A(x)(x(squared) - x) + B(x)(x(power of 4) + 4x(squared) - 4x + 4) = 1