PaperMath’s sum
Contents
PaperMath’s sum
Papermath’s sum states,
Or
For all real values of , this equation holds true for all nonnegative values of
. When
, this reduces to
Proof
First, note that the part is trivial multiplication, associativity, commutativity, and distributivity over addition,
Observing that
and
concludes the proof.
Problems
AMC 12A Problem 25
For a positive integer and nonzero digits
,
, and
, let
be the
-digit integer each of whose digits is equal to
; let
be the
-digit integer each of whose digits is equal to
, and let
be the
-digit (not
-digit) integer each of whose digits is equal to
. What is the greatest possible value of
for which there are at least two values of
such that
?
Notes
Papermath’s sum was named by the aops user Papermath. The name is not widely used.