The Chinese remainder theorem.(a) Make a table with three columns. The first column is all...

The Chinese remainder theorem.

(a) Make a table with three columns. The first column is all numbers from 0 to 14. The second is the residues of these numbers modulo 3; the third column is the residues modulo 5.

(b) Prove that if p and q are distinct primes, then for every pair (j, k) with 0 ≤ j

(c) In this one-to-one correspondence between integers and pairs, it is easy to go from i to (j, k). Prove that the following formula takes you the other way:

(d) Can you generalize parts (b) and (c) to more than two primes?