Daniel's polynomial

Algebra

Suppose \(f\) is a polynomial of degree 7 which satisfies \(f(1)=2\), \(f(2)=5\), \(f(3)=10\), \(f(4)=17\), \(f(5)=26\), \(f(6)=37\), \(f(7)=50.\) What is the value of \(f(0)+f(8)\)?

This problem is shared by Daniel L.