4
votes
3answers
94 views

Question about $T_n = n + (n-1)(n-2)(n-3)(n-4)$

The formula $T_n = n + (n-1)(n-2)(n-3)(n-4)$ will produce an arithmetic sequence for $n < 5$ but not for $n \ge 5$. Explain why. I think it is because if n is less than five the term with ...
2
votes
4answers
114 views

Finding the GCD of $50!$ and $2^{50}$

I've been trying to figure out how $n!$ and $x^n$ are related (where x is an integer) for most of the morning - I know it must be the key to unlocking this problem. Up to this point I've only used ...
4
votes
2answers
242 views

Elements of finite order in the group of arithmetic functions under Dirichlet convolution.

Let $(G, ∗)$ be the group of arithmetic functions $f : N \to C$ that satisfy $f (1)\neq 0$, with group operation given by the Dirichlet product $∗$. The identity function $I$ is the identity element ...