Pollock octahedral numbers conjecture
Encyclopedia
In additive number theory
, the Pollock octahedral numbers conjecture is an unproven conjecture
that every positive integer is the sum of at most seven octahedral number
s. It was first stated in 1850 by Sir Frederick Pollock
, better known as a lawyer and politician but also a contributor of papers on mathematics to the Royal Society
.
Additive number theory
In number theory, the specialty additive number theory studies subsets of integers and their behavior under addition. More abstractly, the field of "additive number theory" includes the study of Abelian groups and commutative semigroups with an operation of addition. Additive number theory has...
, the Pollock octahedral numbers conjecture is an unproven conjecture
Conjecture
A conjecture is a proposition that is unproven but is thought to be true and has not been disproven. Karl Popper pioneered the use of the term "conjecture" in scientific philosophy. Conjecture is contrasted by hypothesis , which is a testable statement based on accepted grounds...
that every positive integer is the sum of at most seven octahedral number
Octahedral number
In number theory, an octahedral number is a figurate number that represents the number of spheres in an octahedron formed from close-packed spheres...
s. It was first stated in 1850 by Sir Frederick Pollock
Sir Frederick Pollock, 1st Baronet
Sir Frederick Pollock, 1st Baronet PC , was a British lawyer and Tory politician.-Background and education:...
, better known as a lawyer and politician but also a contributor of papers on mathematics to the Royal Society
Royal Society
The Royal Society of London for Improving Natural Knowledge, known simply as the Royal Society, is a learned society for science, and is possibly the oldest such society in existence. Founded in November 1660, it was granted a Royal Charter by King Charles II as the "Royal Society of London"...
.