# Few problems - 4

- Find all integers satisfying such that is a divisor of .
- Find the number of ordered pairs of positive integers which satisfy .
- The integer consists of 2017 consecutive nines. A computer calculates . How many nines does the number contain in total ?
- Let be an acute angled triangle such that . Let be a point on such that . Let be an internal point of the segment . Prove that if and only if .
- Let where is an integer. Prove that cannot be expressed as the product of two non-constant polynomials with integer coefficients.