Question

Elucidean Algorithm.

Q 4. For each of the following equations, find a solution z Z or prove that no solution z E Z exists (a) 7x 13 mod 83 mod 624; 11 (b) 25x + 3 (c) 36r 1 mod 87. 12 marks In all cases, explain your reasoning.

Answer 1

(4) 티3 mod 83 12-83 Mulhply ina 13 oo both des ie",7x156三13 mod 83 ) α드43tmod gcd (a, 83):, mod 83 Smcc 커즈13 fe the only soluhon

"To Euchdlean alaor lgoxhwo we need ho hodl Mulh plying g on hotわ ades re, 25 x 200 mod bay cdlas,oa lady)의 oo mod le24) s ne only son

3 mod 31 Since gcal (3b, 8) 3 does not divide се