Three Numbers

Number Theory Level pending

Find the sum of the first three integers greater than 100 such that the product of any two of the three numbers, increased by 1, is a square number.


The answer is 612.

Dr.Alaa Mahmoud by Dr.Alaa Mahmoud , 22, Egypt

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1 solution

Roger Erisman
Apr 22, 2016

In Small Basic:

For i = 101 To 1000

For j = i To 1000 

For k = j To 1000

  a = i*j +1

  b = j*k+1

  c = i*k+1

  If Math.SquareRoot(a) = Math.Floor(Math.SquareRoot(a)) then

 If Math.SquareRoot(b) = Math.Floor(Math.SquareRoot(b)) then

 If Math.SquareRoot(c) = Math.Floor(Math.SquareRoot(c)) then 

   TextWindow.Write(i)

   TextWindow.Write(" ")

   TextWindow.Write(j)

   TextWindow.Write(" ")

   TextWindow.Write(k)

   TextWindow.Write(" ")

   TextWindow.WriteLine(i + j + k)

   EndIf

   EndIf

 EndIf

EndFor

EndFor

EndFor

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