4

Part of 2007 Czech and Slovak Olympiad III A

Problems(1)

the existence of an integer m

Source: Czech and Slovak third round,2007,p4

M=\{1,2,\ldots,2007\}

has the following property: If

n

is an element of

M

, then all terms in the arithmetic progression with its first term

n

and common difference

n+1

M

. Does there exist an integer

m

such that all integers greater than

m

are elements of

M

arithmetic sequencecombinatorics proposedcombinatorics