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 A Pythagorean triangle (Posted on 2016-04-08)
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 Thébault in 1959.

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 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\$

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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