A² + B² = C²

where A=n*X, B=n*(X+1) and C=n*Y.
Determine triples (A,B,C) which satisfy the constraints of n,X,Y noting that A, B and C are all 3 digit numbers when n is 1 through 5.

I think I must be missing something in the formulation of the problem.  We are to assign three-digit integers (presumably not starting with zero) to A, B, and C so that A**2 + B**2 = C**2.

We are also given further constraints on the values of A, B and C.  If we assume that X and Y are positive integers, then B>A, and B - n = A, and all three of A, B, and C must be divisible by ALL of the integers from 1..5 (since n is a factor of each), i.e. they must each be divisible by 60.

This (ignoring the constraint tests) seems to give us only four options for triplet sets:

180, 240, 300 (32400 + 57600 = 90000)

300, 720, 780 (90000 + 518400 = 608400)

360, 480, 600 (129600 + 230400 = 360000)

540, 720, 900 (291600 + 518400 = 810000).

 

None of these seem amenable to the X-Y-n constraints. I read the text as saying that there are values for A, B and C, such that for EACH of the values of n=1..5, the equations are satisfied.

 

Any illumination on this tunnel?

Posted by ed bottemiller on 2008-05-08 15:48:22