Determine hexadecimal-octal and binary representations

Question

i) Use Fermat's Little Theorem to find 3⁵⁰² (mod 503), 3⁵⁰³ (mod 503) and 3⁵⁰⁵ (mod 503).

ii) Write all congruence classes for congruence mod 6, providing most usual and one other name for each.

iii) Determine 242 (mod 15).

iv) Let S be set of all people in world. For a, b E S, state the binary relation R as follows: ( a, b ) E E if and only if a and b have visited same webpage. Is this example of the partially ordered set? Explain why or why not?

iv) Determine binary, octal and hexadecimal representations for 2705.

v) Determine q and r as defined in Division Algorithm when a = 549 and b = 236