Let me give my shot

\(375y=x^2\)

splitting the 375 = \(5^2*5*3\)

now as 375y is a square of positive integer and y is also a positive integer

implies that y has to be = 5*3*a^2, where a is an integer too

Why? let me show

375y=\(5^2*5*3*[5*3*a^2]\) = \(25^2*3^2*a^2\)

\(a^2\) is added so as to generale the possible values of y.

If you don't understand till here try different values of 'a' such as {2,3,4} to get y and x. It will give you different set of values to understand the reason of using a.

Now start with problem

1) \(y/15 = 15*a^2/15 = a^2\)

definitely a integer that too positive

2) \(y/30 = 15*a^2/30 = a^2/2\)

not necessary an integer if a^2 is not a multiple of 2.

3) \(y^2/25 = 15*15*a^4/25 = 9a^4\)

definitely an integer.

(i) and (iii)

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Consider kudos for the good post ...

My debrief : journey-670-to-720-q50-v36-long-85083.html