the perfect numbers are:
*6
*28
*496
the sums are to make 6
1 + 2 +3=6 1,2,3 are the factors of 6
1 + 2 + 4 + 7 + 14 = 28 1,2,4,7 & 14 are the factors of 28
4 + 2 + 1 + 8 + 16 + 31 + 62 + 31 + 62 +124 +248=496
By definition, ALL perfect squares are whole numbers!
Ah, perfect numbers are quite special in the world of mathematics. There are only a few known perfect numbers, and they have a fascinating harmony to them. Less than 50, we have two perfect numbers: 6 and 28. Each of them is the sum of their divisors, creating a beautiful balance in the world of numbers.
6 and 28 are perfect numbers.
All numbers have factors. Some factors are perfect squares. We call these perfect square factors. 9 is a perfect square factor of 27.
81. They are the perfect squares of numbers starting from 5.81. They are the perfect squares of numbers starting from 5.81. They are the perfect squares of numbers starting from 5.81. They are the perfect squares of numbers starting from 5.
There are infinitely many perfect numbers so they cannot all be listed.
By definition, ALL perfect squares are whole numbers!
No. The only perfect numbers less than 100 are 6 and 28. All known perfect numbers are even - it is unknown whether there are odd perfect numbers.
All compound numbers that are not perfect squares.
The perfect numbers less than 100 are 6 and 28.
No.First of all, you can't write negative numbers as sums of perfect squares at all - since all perfect squares are positive.Second, for natural numbers (1, 2, 3...) you may need up to 4 perfect squares: http://en.wikipedia.org/wiki/Lagrange's_four-square_theoremNo.First of all, you can't write negative numbers as sums of perfect squares at all - since all perfect squares are positive.Second, for natural numbers (1, 2, 3...) you may need up to 4 perfect squares: http://en.wikipedia.org/wiki/Lagrange's_four-square_theoremNo.First of all, you can't write negative numbers as sums of perfect squares at all - since all perfect squares are positive.Second, for natural numbers (1, 2, 3...) you may need up to 4 perfect squares: http://en.wikipedia.org/wiki/Lagrange's_four-square_theoremNo.First of all, you can't write negative numbers as sums of perfect squares at all - since all perfect squares are positive.Second, for natural numbers (1, 2, 3...) you may need up to 4 perfect squares: http://en.wikipedia.org/wiki/Lagrange's_four-square_theorem
Yes.
Ah, perfect numbers are quite special in the world of mathematics. There are only a few known perfect numbers, and they have a fascinating harmony to them. Less than 50, we have two perfect numbers: 6 and 28. Each of them is the sum of their divisors, creating a beautiful balance in the world of numbers.
6 and 28
101
All their roots are whole numbers.
1501