Question

Use the extended Euclidean algorithm to express as a linear combination of 245 and 356

Short answer

$\gcd (252,356)=17\cdot \left(356\right)+(-24)\left(252\right)$

Step-by-step solution

Step: 1

a)$a^a=245,b=356$

By Euclidean algorithm,

$$\begin{gathered} 356=1.\left(252\right)+104 \\ 252=2.(104)+44 \\ 104=2.\left(44\right)+16 \\ 44=2.\left(16\right)+12 \\ 16=1.\left(12\right)+4 \\ 12=3.\left(4\right)+0 \end{gathered}$$

Hence$\gcd (252,356)$ has been expressed as a linear combination of the given integers as$\gcd (252,356)=17\cdot \left(356\right)+(-24)\left(252\right)$