SECTION 3.7
8.
1=89*144-55*233
89
10.
If n>1 then sa will not be congruent to l and m.  Because of this, it will not be the modular inverse.
12.
X   12(mod 17)
28a.
3^2 mod5 * (3^4)^75 mod5 = 3^2 mod5 * 1 = 9 mod5 = 4
3^2 mod7 * (3^6)^50 mod7 = 3^2 mod7 *1 = 9 mod7 = 2
3^2 mod11 * (3^10)^30 mod11 = 3^2 mod11 * 1 = 9 mod11 = 9
32.
1729 = 7*13*19
If gcd(b, 1729) = 1, then gcd(b, 7) = gcd(b, 13) = gcd(b, 19) = 1.
 Using FLT, b6   1 (mod 7), b12   1 (mod 13) , and b18   1 (mod 19)
b1728   (b6)288   1 (mod 7)
b1728   (b12)144   1 (mod 13)
b1728   (b18)96   1 (mod 19)
By the CRT, it follows that b1728   1 (mod 1729)
36.
d. 22
h. 19
48.
17*356 – 24*252 = 4