A hypothetical ARML team (which consists of 15 people) somewhere in the middle of someplace are having a practice session. Each student has been assigned a unique nonnegative integer .

At the start of the meeting, the coach opens a box of pizza, but finds it to be empty. He is silent for a moment, then says, "Okay, I was saving a pizza for the meeting. Who ate it!?"

Each student makes a response based on their number :

• If there exists a positive integer such that , then that student makes the statement: "It wasn't me!".
• Otherwise, that student says: "The students with the numbers congruent to and mod 15 is telling the truth.", but makes no statement about themselves.

The coach knows exactly one person is lying, and that that person ate the pizza. (Don't ask me how.) Find, with proof, who ate the pizza.