To find three numbers (A, B, C) in geometrical progression such that

each of B – A, C – B, C – A is a square

A general solution:

[It may not give all possible solutions, though]

Take , ,

If we set the condition,

this condition will be satisfied if

the legs of a pythagorean triple.

the common ratio is,

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I’m choosing to use B – A for this instead of A – B

We can have {a, b, c} = {567, 1008, 1792}

1008 – 567 = 21^2

1792 -1008 = 28^2

1792 – 567 = 35^2

Common ratio is 16/9

Paul.

Good! B – A is a better choice

I posted a general solution. Not all possible solutions are generated