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Q: A number that is greater than one whose only divisors equal one and itself?

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First, you want to know the definition of a perfect number: A perfect number is an integer which is equal to the sum of all its positive integer divisors that are less than itself. Example: The positive integer divisors of 6, less than 6, are 1, 2, and 3. The sum of those divisors is 1 + 2 + 3 = 6. Therefore, 6 is a perfect number. Now, 21 does not meet this definition and therefore is not a perfect number. Let's try it. There are three positive divisors of 21, namely, 1, 3, and 7, that are less than 21, itself. (There are no others.) But the sum of these divisors is 1 + 3 + 7 = 11, which is not equal to 21. Therefore, we confirm that 21 is not a perfect number.

When the number is greater than or equal to zero. e.g. l 5 l = 5

This number is equal to itself, and to no other number.This number is equal to itself, and to no other number.This number is equal to itself, and to no other number.This number is equal to itself, and to no other number.

That means that in the relation considered, any object relates to itself: For any "x", relation(x, x) is true. For example, this is a property of equality (any number is equal to itself), of congruence (any object is congruent to itself), and to relationships such as greater-than-or-equal (any number is greater than or equal to itself) and the non-strict subset relation (any set is a subset of itself).

16 is not a perfect number as defined by Euchlid and Euler. 6 is a perfect number, by their definition, because it is the sum of all its proper positive divisors - all numbers that will divide into the number excluding itself - (1 + 2 + 3) = 6, and equal to half the sum of all its positive divisors, including itself (1 + 2 + 3 + 6)/2 = 6. 28 is the next number. There is still an unsolved mystery in number theory as to whether there can be an odd perfect number.

Related questions

A perfect number is equal to the sum of its proper divisors (the factors excluding the number itself.) 6 is a perfect number. Its proper divisors are 1, 2 and 3.

A perfect number is the term for a number that is equal to the sum of its proper divisors. Be careful not to confuse that with proper factors. Proper divisors include 1 but not the number itself. Proper factors don't include either I or the original number.

An amicable number is one of a pair of numbers which have the property that the sum of the divisors of each, excluding itself, is equal to the other number.

A number is considered perfect if it is equal to the sum of all its positive factors/divisors, excluding itself. These are the first few perfect numbers: * 6 * 28 * 496 * 8128 * 33550336 * 8589869056A perfect number is a positive integer that is equal to the sum of its positive divisors, excluding the number itself. An example 1+2+3=6 and 1x2x3=6

First, you want to know the definition of a perfect number: A perfect number is an integer which is equal to the sum of all its positive integer divisors that are less than itself. Example: The positive integer divisors of 6, less than 6, are 1, 2, and 3. The sum of those divisors is 1 + 2 + 3 = 6. Therefore, 6 is a perfect number. Now, 21 does not meet this definition and therefore is not a perfect number. Let's try it. There are three positive divisors of 21, namely, 1, 3, and 7, that are less than 21, itself. (There are no others.) But the sum of these divisors is 1 + 3 + 7 = 11, which is not equal to 21. Therefore, we confirm that 21 is not a perfect number.

A perfect number is only classified as a perfect number because all of its proper divisors add up to itself. For example, the proper divisors of six are one, two and three. Those numbers added together equal six. Therefore, six is a perfect number.

When the number is greater than or equal to zero. e.g. l 5 l = 5

An integer (call it 'x') has exactly 3 divisors if and only if it is the square of a prime number. In other words, to generate a list of integers with exactly 3 divisors, just keep squaring prime numbers. A number with 3 divisors cannot be prime (a prime number has only 2 divisors, 1 and itself). So it must be a composite number, which is a number that can be factored as a product of prime numbers (Fundamental Theorem of Arithmetic) -- i.e. a composite number must have at least one prime divisor. In the case where the number has only 3 divisors, two of them are 1 and the number itself (neither of which are prime). Therefore the third divisor must be a prime number. So the three divisors of 'x' are: 1, p, x where p is prime. Now since p is a divisor (or factor) of x, and the only other divisor besides 1 and x itself, x must equal p*p -- or x=p^2 . Obvious x can't equal p*x and if x = p*1, x=p so x is prime, or has only 2 divisors... If x = p^(3) , then x = p*p* p , or p*(p^2) ... this means that p^2 would also have to be a divisor of x, and this would contradict with x having only 3 divisors. For the same reason, x = p^(greater than 3) is also not possible. So the only possibility is that an integer with exactly 3 divisors is the square of a prime number "p". The divisors are 1, p, and p^2. I'm sure there's a simpler, more elegant way of explaining this, but it should be clear enough.

When the number is greater than or equal to zero. e.g. l 5 l = 5

This number is equal to itself, and to no other number.This number is equal to itself, and to no other number.This number is equal to itself, and to no other number.This number is equal to itself, and to no other number.

That means that in the relation considered, any object relates to itself: For any "x", relation(x, x) is true. For example, this is a property of equality (any number is equal to itself), of congruence (any object is congruent to itself), and to relationships such as greater-than-or-equal (any number is greater than or equal to itself) and the non-strict subset relation (any set is a subset of itself).

The absolute value of a number equals the number itself if and only if the number is a positive real number (x >= 0 and does not include a nonzero imaginary component).