Polite number

Polite number

A polite number is a positive integer which can be written as the sum of two or more consecutive positive integers. Other positive integers are impolite.citation
last = Adams | first = Ken
date = March 1993
issue = 478
journal = The Mathematical Gazette
pages = 79–80
title = How polite is "x"?
url = http://www.jstor.org/stable/3619263
volume = 77
.] Polite numbers have appeared as a problem on University of Cambridge NRICH website. [citation
date = December 2002
publisher = NRICH
title = Polite Numbers
url = http://nrich.maths.org/public/viewer.php?obj_id=2074
.
] Impolite numbers are exactly all powers of two. [citation
last = Griggs | first = Terry S.
date = December 1991
issue = 474
journal = The Mathematical Gazette
pages = 442–443
title = Impolite Numbers
url = http://www.jstor.org/stable/3618630
volume = 75
.
]

The politeness of a positive number is the number of ways it can be expressed as the sum of consecutive integers.

References


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