IMO 1966 LL ROM29

(a) Find the number of ways 500 can be represented as a sum of

IMO 1966 LL ROM29

Origin: ROM

Problem

(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 \inN. Which of these representations consist only of natural numbers? (c) Determine the number of such representations for an arbitrary natural number N.