MathDB

Putnam 2012 A4

Source:

December 3, 2012

Putnaminequalitiesmodular arithmeticarithmetic sequencecollege contests

Problem Statement

Let

q

and

r

be integers with

q>0,

and let

A

and

B

be intervals on the real line. Let

T

be the set of all

b+mq

where

b

and

m

are integers with

b

in

B,

and let

S

be the set of all integers

a

in

A

such that

ra

is in

T.

Show that if the product of the lengths of

A

and

B

is less than

q,

then

S

is the intersection of

A

with some arithmetic progression.

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