Number theory practice problems
1. Solve the congruence:
10x 12(mod 40)
2. Solve the congruence:
35x 21(mod 98)
3. Solve the system of congruences:
a 2(mod 6)
a 3(mod 7)
a 4(mod 15)
4. List all squares modulo: 11; 12; 13.
5. Is 1 a square modulo 7? 11? 31
Answers or hints to some practice problems.
3. The first and the third imply: x 2(mod 3) and x 1(mod 3).
Therefore there are no solutions. Actually, I meant to make it an
example on the Chinese remainder theorem like in the last quiz, but
made an error. T
Solutions to number theory practice problems
12. A message is a residue P modulo 17. The encoding procedure is
C = P 5 ( mod 17). Encode the messages P = 2, P = 3, P = 4. What
is the decoding procedure?
P = 2, C = 32 15; P = 3, C = 27 9 10 9 = 90 5;
P = 4