(See attached file for full problem description)
We consider the special case when m=3 and n=5.
(a) Find the explicit function from the Chinese Remainder Theorem Chapter summary. (Recall that g is the inverse function of f.)
(b) Write down all ordered pairs (a,b) Є .
(c) Compute g(a,b) for each ordered pair in part (b), reducing each answer to its remainder modulo 15.
(d) Compare the list in part (c) with the integers modulo 15 which are relatively prime to 15.
Note: In this discussion will be the function defined in the chapter summary for the Chinese Remainder Theorem given by .
Note: g is defined as follows:
Where is the multiplicative inverse of m1 modulo m2 and conversely.
This solution is comprised of a detailed explanation to find the explicit function from the Chinese Remainder Theorem Chapter summary.