Difference between revisions of "PaperMath’s sum"
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==Notes== | ==Notes== | ||
− | Papermath’s sum was named by the aops user Papermath. The name is not widely used. | + | Papermath’s sum was named by the aops user Papermath, after noticing it in a solution to an AMC 12 problem. The name is not widely used. |
==See also== | ==See also== | ||
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*[[Cyclic sum]] | *[[Cyclic sum]] | ||
*[[Summation]] | *[[Summation]] |
Latest revision as of 23:33, 1 September 2024
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, after noticing it in a solution to an AMC 12 problem. The name is not widely used.