Number theory : Using the extended version of Euclid’s algorithm, find a solution to the following Dio-phantine linear equation.

Number theory.

1.Using the extended version of Euclid’s algorithm, find a solution to the following Dio-phantine linear equation.
77x + 91y + 143z = 2 [10]

2. Find all solutions for the following pair of simultaneous congruences.
               262x 3 mod 807
               3x 2 mod 5

Instructions for completing the examination:

Show all your workings.