Question 64
A finite sequence of integers $a_0,a_1,\dots,a_n$ is quadratic if for each $i=1,2,\dots,n$, $|a_i-a_{i-1}|=i^2$.
a. Show that for any two integers $b,c$, $b\lt c$, there exists a natural number $n$ and a quadratic sequence with $a_0=b$, $a_n=c$.
b. Find the smallest natural number $n$ for which there exists a quadratic sequence with $a_0=0$ and $a_n=2012$.
a. Show that for any two integers $b,c$, $b\lt c$, there exists a natural number $n$ and a quadratic sequence with $a_0=b$, $a_n=c$.
b. Find the smallest natural number $n$ for which there exists a quadratic sequence with $a_0=0$ and $a_n=2012$.