# Problems for the week

#### Problem 1.

Determine all positive integers such that,

for some , where is the number of divisors of .

#### Problem 2.

Find the first digit before and after the decimal point in . (without using a calculator)

#### Problem 3.

points are chosen on a circle. In how many ways can you join pairs of points by nonintersecting chords?

#### Problem 4.

Let be a function, continuous on [a,b] and differentiable on (a,b). Prove that if there exists such that

then there exists such that

### 1 Comment

• Jakir Sarif Mondal