Question 29
(ROM) (a) Find the number of ways $500$ can be represented as a sum of consecutive integers.
(b) Find the number of such representations for $N=2^\alpha3^\beta5^\gamma$, $\alpha,\beta,\gamma\in\mathbb N$. Which of these representations consist only of natural numbers?
(c) Determine the number of such representations for an arbitrary natural number $N$.
(b) Find the number of such representations for $N=2^\alpha3^\beta5^\gamma$, $\alpha,\beta,\gamma\in\mathbb N$. Which of these representations consist only of natural numbers?
(c) Determine the number of such representations for an arbitrary natural number $N$.