Question

For how many integers n if (n/(20-n)) the square of an integers

Answer 1

Firstly, (n / (20 - n) )  is a perfect square .'. (n / (20 - n) )∉ $Z^{-}$
=> n ∉  $Z^{-}$

Now, (n / (20 - n) ) [max] = 19 for n=19...
.'. for (n / (20 - n) )  to be a perfect square, (n / (20 - n) ) ∈ ( 1, 4, 9, 16 )
Now, 
equating the relations, we get ::
n ∈ ( 10 , 16, 18, 320/17 )
Therefore, we see, there are 3 Integral values for n for which (n / (20 - n) )  is a perfect square...


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Answer 2

Answer:

there are 4 such integers

Step-by-step explanation:

if we go by hit and trial we get that 0,10,16,18 are the possible values of n.

which makes n/(20-n) the square of 0,1,2,3 respectively.