Answer Happy

1. Solve the following linear congruence in two variables. Find all incongruent solutions 8r+ 2y 4 mod 10. Hint: rewrite as 8x = 4-2y mod 10 and solve the linear congruence in one variable obtained by successively setting y equal to 0,1,2..... 2. Fifteen pirates steal a sack of gold coins of equal value. The pirates attempt to divide the coins evenly but find that two coins are left over. A quarrel over the two coines erpts and one pirate is sent way. Another attempt to divide the coins is made, but now I coin is left over. Another quarrel erupts and one more pirate is sent away. A third attempt to divide the coins evenly succeeds. Find the smallest number of gold coins that could have been in the sack. (You may use a calculator for the final answer.) <