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A Pythagorean triangle (Posted on 2016-04-08) Difficulty: 4 of 5
Given: The sum of the squares of a and its reverse b (i.e. the number read from right to left) is a perfect square.

Find the sides a,b,c of this peculiar right-angled triangle.

Source: This property was discovered by Victor Th├ębault in 1959.

No Solution Yet Submitted by Ady TZIDON    
Rating: 5.0000 (1 votes)

Comments: ( Back to comment list | You must be logged in to post comments.)
Solution computer solution | Comment 1 of 4
Searching up through 7-digit numbers, the program finds three solutions:

   Numbers                                         Squares

88209 90288 126225     7780827681 8151922944 15932750625
90288 88209 126225     8151922944 7780827681 15932750625

125928 829521 839025     15857861184 688105089441 703962950625
829521 125928 839025     688105089441 15857861184 703962950625

5513508 8053155 9759717     30398770466064 64853305454025 95252075920089
8053155 5513508 9759717     64853305454025 30398770466064 95252075920089

DefDbl A-Z
Dim crlf$


Private Sub Form_Load()
 Form1.Visible = True
 
 Text1.Text = ""
 crlf = Chr$(13) + Chr$(10)
 
 For a = 1 To 9999999
   DoEvents
   ast$ = LTrim(Str(a))
   b = 0
   For i = Len(ast) To 1 Step -1
     b = b * 10 + Val(Mid(ast, i, 1))
   Next
   csq = a * a + b * b
   sr = Int(Sqr(csq) + 0.5)
   If sr * sr = csq And Len(ast) = Len(LTrim(Str(b))) Then
     '(the length check prevents trailing zero from becoming a non-showing leading zero)
     c = sr
     Text1.Text = Text1.Text & a & Str(b) & Str(c) & "    " & Str(a * a) & Str(b * b) & Str(c * c) & crlf
   End If
 Next
 
 Text1.Text = Text1.Text & crlf & " done"
  
End Sub

Edited on April 8, 2016, 7:23 pm
  Posted by Charlie on 2016-04-08 19:21:59

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