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Quadratic Expressions, Perfect Square Not (Posted on 2010-01-03) Difficulty: 2 of 5
Prove that there cannot exist any positive integer x, such that each of 2x2 + 1, 3x2 + 1 and 6x2 + 1 is a perfect square.

See The Solution Submitted by K Sengupta    
Rating: 3.5000 (2 votes)

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Some Thoughts re: Pell's ( Bramagupta's) equation | Comment 1 of 6

In 1768, Lagrange gave the first complete proof of the solvability of
x2 - Dy2 = 1  ( complicated)

I erased a wrong statement - please see my next post

OUT OF THE  THREE GIVEN EQUATIONS WE CAN FULLFIL THE FIRST  AND THE LAST e.g. D=2 y=2 =>>x^2=1+8=9   OK
D=6 y=2  ==>>x^2=1+24=25               OK
but not the second x^2=1+12=13   NOT A SQUARE

Rem: puzzle's x is our y ; D=2,3,6

Edited on January 10, 2010, 1:13 pm
  Posted by Ady TZIDON on 2010-01-03 19:41:01

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