Homework for Week 4
- (Rotman 1.91) Find all solutions to the simultaneous congruences:
- x=2 mod 5 and 3x = 1 mod 8;
- 3x=2 mod 5 and 2x=1 mod 3.
- (Rotman 1.95) Find all solutions to the linear system
x = 12 mod 25
x = 2 mod 30.
- Show that if a = r0 + 1000 r1+10002 r2 + 10003r3+ ... then a is divisible by 7 if and only if r0 - r1+r2-r3+... is divisible by 7.
- Which of the following are valid bit-parity-check codewords (explain): 0110101, 010110, 1101101101?
- Which of the following are valid ISBN codes (explain): 0-14-235213-9, 11-2463-253-7, 0-471-43809-X?
- Write the permutation (134)(25) in one-line notation, arrow notation, and two-line notation.
- Write the permutation 21435 in two-line notation, cycle notation, and arrow notation.
- Let u = (134)(25) and v = 21435. Compute uv and vu. Compute the inverse of u and the inverse of v.
Due Tuesday 2/17