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
the squares of 10 though 22 are all three digit numbers under 500. though none of the sums of their digits total an even multiple of 15.
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.
the squares of 10 though 22 are all three digit numbers under 500. though none of the sums of their digits total an even multiple of 15.
No, the natural numbers are not closed under division. For example, 2 and 3 are natural numbers, but 2/3 is not.
The best trick for this is to think of averages. Put the 1 with 500, 2 with 499,, 3 with 488, ... On average these numbers are (1 + 500)/2 or 250.5 So you want to add up 500 numbers each of which is, on average 250.5 The answer is 500 x 250.5 which is 125250