Each integer in Zn represents a residue class or congruence class.
(a) Define the set of congruence classes of (mod 15).
(b) List the congruence classes (mod 15).
(c) A certain country M has a National Arena with seating capacity of 6,000. As
part of the government's effort to stem the occurrence of cruelty to children in
that country, it has been designated that citizens will be allowed to attend a
parenting seminar at the National Arena. For ease of reference, each seat at
the National Arena is uniquely assigned the Parenting Seat Number (PST)
0, 1, 2, 3, ..., 5999.
Citizens with a Tax Registration Number (TRN) will be randomly picked to
attend the event and receive a unique bank transfer deposit. The citizen is
assigned one of the PST based on the unique 9-digit TRN number and the
result of the hashing function $f$. The TRN is designated as $T$ and the
hashing function $f$ is defined as
$f(T) = T \mod 6000$.
Andrew Brotherton Campbell Dennis with Tax Registration Number
196178150 is picked for the parenting seminar. By simplifying the TRN to a
set of addition(s) and multiplication(s) of positive integers, apply the
principles of modular arithmetic and illustrate to which Parenting Seat
Number would be initially assigned before adjustment for clashing.
