Answer the exercises completely, showing all your work and
computations.
(1) Prove that
(−1)p−1
2 −[ p4 ] = (−1)
p2−1
8
when p ≡ 5 mod 8 and when p ≡ 7 mod 8.
(2) Do exercise 1, part (d) from section 4.1 (page 106) in the
textbook.(3) Do exercise 12, part (b) from section 4.2 (page 115)
in the textbook.(4) Do exercise 13, part (b) from section 4.2 (page
116) in the textbook.(5) Do exercise 14, parts (b)(d)(f) from
section 4.2 (page 116) in the textbook.(6) Do exercise 15, from
section 4.2 (page 116) in the textbook.(7) Do exercise 17, from
section 4.2 (page 116) in the textbook.(8) Do exercise 28, parts
(b)(d)(f) from section 4.3 (page 124) in the textbook.(9) Do
exercise 32, from section 4.3 (page 125) in the textbook.
