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.