Question 21
N3 (BUL) A finite sequence of integers $a_0,a_1,\ldots,a_n$ is called quadratic if for each $i\in\{1,2,\ldots,n\}$ we have the equality $|a_i-a_{i-1}|=i^2$.
(a) Prove that for any two integers $b$ and $c$, there exist a natural number $n$ and a quadratic sequence with $a_0=b$ and $a_n=c$.
(b) Find the smallest natural number $n$ for which there exists a quadratic sequence with $a_0=0$ and $a_n=1996$.
(a) Prove that for any two integers $b$ and $c$, there exist a natural number $n$ and a quadratic sequence with $a_0=b$ and $a_n=c$.
(b) Find the smallest natural number $n$ for which there exists a quadratic sequence with $a_0=0$ and $a_n=1996$.