Bunuel wrote:
The product of the squares of two positive integers is 400. How many pairs of positive integers satisfy this condition?
A. 0
B. 1
C. 2
D. 3
E. 4
We can express 400 as a product of two numbers:
400 = 1 x 400 = 2 x 200 = 4 x 100 = 5 x 80 = 8 x 50 = 10 x 40 = 16 x 25 = 20 x 20
We see that of the products above, three products are products of two perfect squares:
1 x 400 = 1^2 x 20^2
4 x 100 = 2^2 x 10^2
16 x 25 = 4^2 x 5^2
Thus, there are 3 pairs of positive integers that satisfy the condition.
Alternate
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