MathDB

A finite sequence of integers

a_0, a_1, \ldots, a_n

is called quadratic if for each

i

in the set

\{1,2 \ldots, n\}

we have the equality |a_i \minus{} a_{i\minus{}1}| \equal{} i^2. a.) Prove that any two integers

b

and

c,

there exists a natural number

n

and a quadratic sequence with a_0 \equal{} b and a_n \equal{} c. b.) Find the smallest natural number

n

for which there exists a quadratic sequence with a_0 \equal{} 0 and a_n \equal{} 1996.

Problem Statement