MathDB

31

Part of PEN P Problems

Problems(1)

P 31

Source:

5/25/2007
A finite sequence of integers a0,a1,⋯ ,ana_{0}, a_{1}, \cdots, a_{n} is called quadratic if for each i∈{1,2,⋯ ,n}i \in \{1,2,\cdots,n \} we have the equality ∣ai−ai−1∣=i2\vert a_{i}-a_{i-1} \vert = i^2. [*] Prove that for any two integers bb and cc, there exists a natural number nn and a quadratic sequence with a0=ba_{0}=b and an=ca_{n}=c. [*] Find the smallest natural number nn for which there exists a quadratic sequence with a0=0a_{0}=0 and an=1996a_{n}=1996.
quadraticsAdditive Number Theory