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Surprising Sudden Square (Posted on 2007-03-24) Difficulty: 3 of 5
Prove that if a²+b² is a multiple of ab+1, for positive integer a and b, then (a²+b²)/(ab+1) is a perfect square.

No Solution Yet Submitted by Old Original Oskar!    
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Some Thoughts an observation | Comment 8 of 10 |

Proving that "if a2+b2 is a multiple of ab+1, for positive integer a and b, then (a2+b2)/(ab+1) is a perfect square" is a little beyond my current mathematical skill. But here is proof that when a = b3 (for positive integer a and b) it can be seen that (a2+b2)/(ab+1) = b2.

Substituting b3 for a, ((b3)2+b2)/((b3)*b+1) = b2
--> (b6 + b2) = b2*(b4 + 1)
--> (b6 + b2) = b6 + b2


  Posted by Dej Mar on 2007-03-25 21:02:08
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