MathDB

The positive integer

k

and the set

A

of distinct integers from

1

3k

inclusively are such that there are no distinct

a

b

c

A

satisfying

2b = a + c

. The numbers from

A

in the interval

[1, k]

will be called small; those in

[k + 1, 2k]

- medium and those in

[2k + 1, 3k]

- large. It is always true that there are no positive integers

x

and

d

such that if

x

x + d

, and

x + 2d

are divided by

3k

then the remainders belong to

A

and those of

x

and

x + d

are different and are: a) small?

\hspace{1.5px}

b) medium?

\hspace{1.5px}

c) large? (In this problem we assume that if a multiple of

3k

is divided by

3k

then the remainder is

3k

rather than

0

Problem Statement