Part 2’s link https://nttuan.org/2016/11/13/topic-832/
Problem 9. Let and be fixed integers each at least . Find the largest positive integer for which there exists a polynomial , of degree and with rational coefficients, such that the following property holds: exactly one of is an integer for each .
Problem 10. Let be a polynomial. Prove that we have an .
Problem 11. Let be the Fibonacci sequence and the polynomial of degree satisfying