Proper divisor: Difference between revisions
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proper divisors of 1, positive integers |
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A '''proper divisor''' of a [[positive integer]] <math>n</math> is any [[divisor]] of <math>n</math> other than <math>n</math> itself. Thus, [[prime number]]s have exactly one proper divisor | A '''proper divisor''' of a [[positive integer]] <math>n</math> is any [[divisor]] of <math>n</math> other than <math>n</math> itself. Thus <math>1</math> has no proper divisors, [[prime number]]s have exactly one proper divisor <math>1</math>, and all other positive integers have at least two proper divisors. | ||
== See Also == | |||
*[[Deficient number]] | |||
*[[Abundant number]] | |||
*[[Perfect number]] | |||
*[[2017 USAJMO Problems/Problem 4]] | |||
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Latest revision as of 15:27, 10 May 2021
A proper divisor of a positive integer 
is any divisor of other than itself. Thus 
has no proper divisors, prime numbers have exactly one proper divisor , and all other positive integers have at least two proper divisors.
See Also
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