tags: MATA02-2022

Ungraded problems 8

You are to work on these questions only for the benefit of learning the material. These problems are meant for practice, not an assignment to be handed in.

1.

Find the following quotients:

1. $3/5$ mod 11
2. $4/3$ mod 13
3. $3/4$ mod 13
4. $4/3$ mod 17
5. $3/4$ mod 17

2.

Consider the expression

$\frac{2\times 3}{5}$ mod 17. Evaluate this four ways:

1. Find
   $\frac{1}{5}$ mod 17, that is, find
   $x$ so that
   $5x\equiv 1$ mod 17, and then multiply
   $x$ by 2 and by 3.
2. Find
   $\frac{2}{5}$ mod 17, that is, find
   $x$ so that
   $5x\equiv 2$ mod 17, and multiply
   $x$ by 3.
3. Find
   $\frac{3}{5}$ mod 17, that is, find
   $x$ so that
   $5x\equiv 3$ mod 17, and multiply
   $x$ by 2.
4. Find
   $\frac{6}{5}$ mod 17, that is, find
   $x$ so that
   $5x\equiv 6$ mod 17.

Selected (partial) solutions

Solutions to selected problems (click to expand)

1.1: 9
1.2: 10
1.3: 4
1.4: 7
1.5: 5

2: 8