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Hint: look at the factorizations of the first 10 positive whole numbers and see which number has an odd number of factors
I'll look and see... wait a second
From 1-10 would only be the number 1; srry I kinda had to go do something for a sec
you sure only 1 has an odd number of factors?
what do you notice
Can't really think of anything
Can you give me a hint?
1, 4, 9, ... hmm
what kind of sequence is that
if you're not sure, look at the next ten numbers (11 through 20) and take note which numbers have an odd number of factors
Sounds like +3, +5, maybe then +7
Yup this works:)
that's one way to look at it, but there's another
the extended sequence is 1, 4, 9, 16, 25, 36, 49, ...
each number is a perfect _____
Oh I didn't notice that
so all you have to do is count the number of perfect squares less than 2000 use this list: http://www.mathwarehouse.com/arithmetic/numbers/list-of-perfect-squares.php or you can take the square root of 2000 to get 44.7213595499958 this means that 44^2 = 1936 is the largest perfect square that is less than 2000 anything higher (like 45^2) is going to be over 2000
On this problem I'm supposably not supposed to use a list, so if 44^2 is the largest perfect square does that mean that I should count all the perfect squares 44^2 and below?
yep, so 1^2, 2^2, 3^2, ..., 41^2, 42^2, 43^2, 44^2 all work
Would 1^3 work too though?
1^2 = 1 is a perfect square
1 only has 1 factor (itself), so it has an odd number of factors
1^3 is still 1, but technically not the same
because if you cubed 2, you would get 2^3 = 8, but 8 doesn't have an odd number of factors
Oh, so 44 positive integers or is it more complicated than what I'm thinking?
yep 44 is your answer and maybe you are, but that's ok, you're thinking about the problem