How many pairs of positive integers $(x,y)$ are there which lie below the graph of the hyperbola $xy = 16$?
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.
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!
Its not infinite. Its finite. Basically, its 0<xy<16.
its 45 when you count it
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.
Yes, the answer is 45
Hmm... I got 46. Though I do think 45 is correct; I must've had a miscalculation. Nice explanation, Overseer! :)
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...
restrict
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?