Asked by rui rui

How many pairs of positive integers $(x,y)$ are there which lie below the graph of the hyperbola $xy = 16$?
Answered by Steve
infinitely many.

Or did you want to restrict the available area?

In the first quadrant, (4,4) is on the curve.

There will be none to the left of (1,16) or to the right of (16,1).

And don't count the lattice points on the curve...
Answered by clache
restrict
Answered by Steve
do you see what a useless response that is? Restrict how?

Anyway, I gave you the information you need.

How about showing some effort of your own here?
Answered by godmodexd
its 45 when you count it
Answered by ajdskf;
Its not infinite. Its finite. Basically, its 0<xy<16.
Answered by Overseer
The answer 45 is correct. You simply find all pairs of integers x and y that multiply to a product greater than zero and less than sixteen.
Answered by Bob
The problem is restricted to x and y being positive integers - no other restrictions are needed. You can allow an infinite area, the answer is still 45.
Answered by Dog_Lover
Hmm... I got 46. Though I do think 45 is correct; I must've had a miscalculation. Nice explanation, Overseer! :)
Answered by Dog_Lover
Oh, I just found a new way to solve it. And wow, this is an old problem :')

But you can just put x in the equation for everything between 1 and 16, then find the y values and add them up. Got me 45!
Answered by IDK
Yes, the answer is 45
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