4.
4
I am pretty sure you can figure this out on your own. Raise different numbers to the square, until you get a 4-digit result. Similary, calculate the cube of different numbers, until you get a 4-digit number. If you want the SAME number to be both a perfect square and a perfect cube, then it must be a power of 6. In that case, just experiment raising different numbers to the sixth power, until you get a 4-digit number.
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
Almost perfect numbers refer to numbers whereσ(x) = 2x - 1, where σ is the sum of divisors function. Any number in the form 2n is almost perfect becauseσ(2n) = 1 + 2 + 4 + ... + 2n = 2n+1-1 = 2(2n) - 1.It is unknown whether any other almost perfect numbers exist.
No.
4.
No. Square numbers (or perfect square numbers) are squares of integers. The perfect square numbers are 1, 4, 9, 16, 25, 36 ... 20 is not in the series.
4
4
no, 10 is not a perfect square. in order for a number to be a perfect square, you have to see if the numbers that are multiplied to get it are the same. for example: 2x2=4; 4 is a perfect square. 12x12=144; 144 is also a perfect square 5x2=10 or 10x1=10. 10 isn't a perfect square because 5 and 2, and 10 and 1, are different numbers.
I am pretty sure you can figure this out on your own. Raise different numbers to the square, until you get a 4-digit result. Similary, calculate the cube of different numbers, until you get a 4-digit number. If you want the SAME number to be both a perfect square and a perfect cube, then it must be a power of 6. In that case, just experiment raising different numbers to the sixth power, until you get a 4-digit number.
They are all perfect square numbers.
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
Almost perfect numbers refer to numbers whereσ(x) = 2x - 1, where σ is the sum of divisors function. Any number in the form 2n is almost perfect becauseσ(2n) = 1 + 2 + 4 + ... + 2n = 2n+1-1 = 2(2n) - 1.It is unknown whether any other almost perfect numbers exist.
6 and 28 are perfect numbers.
There are 48 different numbers that are considered to be perfect numbers. The perfect numbers that are up to 100 include 6 and 28.