Perfect squares are the result of multiplying integers by themselves: 1 x 1 = 1 2 x 2 = 4 3 x 3 = 9 etc. The perfect squares, above, are the numbers to the right of the equal sign, so just continue until you pass the number 500.
You'll need five. 2 x 2 x 5 x 5 x 5 = 500
To find a 3-digit number that meets these criteria, we first need to identify the square numbers under 500. The square numbers under 500 are 1, 4, 9, 16, 25, 36, 49, 64, 81, 100, 121, 144, 169, 196, 225, 256, 289, 324, 361, 400, 441, and 484. Next, we look for even square numbers that have a sum of digits divisible by 15. The only number that meets all these criteria is 324, which is 18 squared.
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
3
The 3 digit numbers under 500 are 100 through 499.
Perfect squares are the result of multiplying integers by themselves: 1 x 1 = 1 2 x 2 = 4 3 x 3 = 9 etc. The perfect squares, above, are the numbers to the right of the equal sign, so just continue until you pass the number 500.
There are 417 of them and it would take too long to list them all. You could draw up a list of all 500 numbers and then delete each multiple of 6. There are 83 of them.
There are 232 numbers between 1 and 500 that are divisible by 3 or 5.
No.
You'll need five. 2 x 2 x 5 x 5 x 5 = 500
1000 (2)1500 (3)
1500
400 of them.
No, the natural numbers are not closed under division. For example, 2 and 3 are natural numbers, but 2/3 is not.
To find a 3-digit number that meets these criteria, we first need to identify the square numbers under 500. The square numbers under 500 are 1, 4, 9, 16, 25, 36, 49, 64, 81, 100, 121, 144, 169, 196, 225, 256, 289, 324, 361, 400, 441, and 484. Next, we look for even square numbers that have a sum of digits divisible by 15. The only number that meets all these criteria is 324, which is 18 squared.
The sum of the first 500 positive integers is: 1 + 2 + 3 + ... + 498 + 499 + 500 = 125250