Find an integer x for which x 1 mod 13 and x 11SolutionUsi

Find an integer x for which x = 1 (mod 13) and x = 11.

Solution

Using Chinese Remainder Theorem:   

X = 1.23(1/23)₁₃ +11.13(1/13)₂₃

solve this you will find the ans.

other Solution: We can easily find a linear combination of 13 and 23 that equals 1, by just writing (4)(23) + (7)(13) = 1. Using the method outlined in the proof of Theorem 1.3.6, the solution is x (1)(4)(23) + (11)(7)(13) = 909 (mod 253).