Good Numbers
Algebra
Level
2
Let a natural number \( n \) be good if there exist two distinct non-integral real numbers \( a \) and \( b \) such that \( a^k - b^k \) is an integer for all \( 1 \leq k \leq n \).
Find the number of natural numbers which are not good.
by
Siddhartha Srivastava