Step 1
Here, we have to solve for congruences
2x=1 mod 5
x=3 mod 4
To solve such questions, we apply chinese remainder theorem.
Chinese Remainder Theorem- Let m, n are relatively prime integers. Then the system of simultaneous congruences has a unique solution modulo M = mxn, for any given integers .
Step 2
and we have x = 3 mod 4
Here, 4 and 5 are co-prime, therefore By chinese remainder theorem, it has unique solution module 20.
So, only possibilty is x=23 which satisfy the given congruences.
Step 3
Answer:
x=23