1. How Many solutions (x,y) are there to the equation 53x + 26y = 88 mod 97?
2. Find x if 3*x = 4 mod 7.
3. Find all x such that 2x = 4 mod 6
4. List all lines which go through (0,3) and (2,3) mod 6.
4. List all points on the line x =3 mod 5.
5. List all the lines in mod 7 which pass through the point (2,3).
6. Suppose a tournament has 24 players and 36 games, with each player playing
in 6 games, and each game containing an equal number of players. How many
players are in each game.
7. Suppose x^4 + x^3 +1 is irreducible in mod 2. Let r be a root of this
polynomial.
a. How large is the new field when we include t.
b. Compute t^3 * (t^2+t+1) in the field.
c. How many lines are there in this new field? How many points on a line?
8. How many lines are there in mod 37?
9. Show x^2 +2 is irreducible mod 5.
10. Suppose we construct a tournament with 25 players with C total contests,
and 5 players in each contest. Each player, and each pair of players appears
in the same number of contests. Explain why each player is in C/5 contests,
and each pair is in C/30 contests.