Question 96
For $n\in\mathbb N$, let
$$S_n=\left\{\binom nn,\binom{2n}n,\binom{3n}n,\ldots,\binom{n^2}n\right\}.$$
a) Prove that infinitely many composite positive integers $n$ have $S_n$ not a complete residue system modulo $n$.
b) Prove that infinitely many composite positive integers $n$ have $S_n$ a complete residue system modulo $n$.
$$S_n=\left\{\binom nn,\binom{2n}n,\binom{3n}n,\ldots,\binom{n^2}n\right\}.$$
a) Prove that infinitely many composite positive integers $n$ have $S_n$ not a complete residue system modulo $n$.
b) Prove that infinitely many composite positive integers $n$ have $S_n$ a complete residue system modulo $n$.