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RMS Rigor (Posted on 2014-11-04) Difficulty: 3 of 5
A < B < C < D are four positive integers such that:

(i) B is the arithmetic mean of A and C and:
(ii) C is the rms of B and D, and:
(iii) D-A = 50

Determine all possible quadruplets satisfying the given conditions and prove that there are no others.

No Solution Yet Submitted by K Sengupta    
Rating: 4.0000 (1 votes)

Comments: ( Back to comment list | You must be logged in to post comments.)
Some Thoughts computer check of all a from 1 to a million (spoiler) | Comment 1 of 4
 For a = 1 To 1000000
   d = a + 50
   For c = a + 2 To a + 48 Step 2
      b = (a + c) / 2
      rmssq = (b * b + d * d) / 2
      If rmssq = c * c Then
        Text1.Text = Text1.Text & a & Str(b) & Str(c) & Str(d) & crlf
        DoEvents
      End If
   Next c
 Next a

finds only

29 47 65 79 as the values of a, b, c and d respectively.

  Posted by Charlie on 2014-11-04 20:32:00
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