Fifteen pirates steal a stack of identical gold coins. when they try to divide them evenly, two coins are left over. a fight erupts and one of the pirates is killed. the remaining pirates try again to evenly distribute the coins. this time there is one coin left over. a second pirate is killed in the resulting argument. now when the remaining pirates try to divide the coins evenly there are no coins left over. use the chinese remainder theorem to find the smallest number of coins that could have been in the sack.

in geometry, parallel lines are lines in a plane which do not meet; that is, two lines in a plane that do not intersect or touch each other at any point are said to be parallel. by extension, a line and a plane, or two planes, in three-dimensional euclidean space that do not share a point are said to be parallel.

sample answer: you can determine whether each element of the domain is paired with exactly one element of the range. for example, if given a graph, you could use the vertical line test; if a vertical line intersects the graph more than once, then the relation that the graph represents is not a function.