Polite number

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A polite number is a number which can be written as the sum of two or more consecutive positive integers. Other numbers are impolite.[1]. Polite numbers have appeared as a problem on University of Cambridge NRICH [2] website and have been used as a topic for mathematical investigations.

Impolite numbers [3] are exactly all powers of two; it can be shown that every polite number is a product of two natural numbers larger than 2; at least one of them is always odd. It can also be shown that all odd prime numbers are polite.

The politeness of a positive number is the number of ways it can be expressed as the sum of consecutive integers [1]

[edit] References

  1. ^ a b Ken Adams (1993) 77.2 How Polite Is x? The Mathematical Gazette, Vol. 77, No. 478 (Mar., 1993), pp. 79-80 (article consists of 2 pages) Published by: The Mathematical Association
  2. ^ NRICH [1]
  3. ^ Terry S. Griggs (1991)75.44 Impolite Numbers The Mathematical Gazette, Vol. 75, No. 474 (Dec., 1991), pp. 442-443
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