SOLUTION: A math teacher collects old books. One day, a student asked him how many old math books he has. He replied, "If I divide the books into unequal whole numbers, then 64 times the d

Question 197753: A math teacher collects old books. One day, a student asked him how many old math books he has. He replied, "If I divide the books into unequal whole numbers, then 64 times the difference between the two numbers equals the difference between the squares of the two numbers." How many old math books does the teacher have?
Answer by josmiceli(19441) (Show Source): You can put this solution on YOUR website!
Call the larger number
Call the smaller number
given:

I now know that the sum of the numbers is
I can think of the right side of the equation as
(hypotenuse)^2 - (one leg)^2 of a right triangle
where is the hypotenuse and is the leg
The left side of the equation must be
where
From above, , so

must be a whole number, since the right side
of the original equation is a whole number
That means that must be a whole number
Note that if , then and
, , and that is
not allowed by the problem.
So
I'll try

Not allowed, since has to be a whole number
I'll try

So,

---------------

The teacher had 64 old math books
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