# The Problem of the week

1. About the problem of the week.

Each Friday the Fall and spring semesters, we will post a problem to encourage undergraduate students to enjoy mathematics outside of the classroom. If you have a solution and want to be a part of it, you may e-mail your solution to Jaiung Jun (jjun@math.binghamton.edu) by Thursday (a day before new problems). We will post solutions (from us) as well as novel solutions from students and record the names of students who've got the most number of novel solutions throughout each semester.

Announcements

1. We will post the solution and winners for the first problem soon.

2. When you submit your answer, please provide some detailed solution rather than just an answer. Also, please include your major and the year you are in so that we can record.

**Problem 2 (Feb 17, 2017)**

A function f(x) from real numbers to real numbers has a continuous second derivative and satisfies the following condition: **2f(x+1)=f(x)+f(2x)** for any real number x. Suppose that f(0)=1. What is f(x)?

**Problem 1 (Feb 13, 2017)**

Circle A rolls one time around circle B whose radius is three times that of circle A. A letter A is drawn inside circle A. How many times will the letter A rotate? (Hint: It's not 3)