MathDB

P 31

Source:

May 25, 2007

quadraticsAdditive Number Theory

Problem Statement

A finite sequence of integers

a_{0}, a_{1}, \cdots, a_{n}

is called quadratic if for each

i \in \{1,2,\cdots,n \}

we have the equality

\vert a_{i}-a_{i-1} \vert = i^2

. [*] Prove that for any two integers

b

and

c

, there exists a natural number

n

and a quadratic sequence with

a_{0}=b

and

a_{n}=c

. [*] Find the smallest natural number

n

for which there exists a quadratic sequence with

a_{0}=0

and

a_{n}=1996

.

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