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Arithmetic progression of second order

Source:

April 26, 2010

number theory proposednumber theory

Problem Statement

Let

(b_n)_{n \ge 0}=\sum_{k=0}^{n} (a_0+kd)

for positive integers

a_0

and

d

. We consider all such sequences containing an element

b_i

which equals

2010

. Determine the greatest possible value of

i

and for this value the integers

a_0

and

d

.
(41th Austrian Mathematical Olympiad, regional competition, problem 4)