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Linear and Quadratic Puzzle (Posted on 2015-06-18) Difficulty: 3 of 5
Determine all possible integers x, y and z such that:
x2 + y2 + z2 = 2(yz + 1) and:
x + y + z = 4018

No Solution Yet Submitted by K Sengupta    
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re: Solution / Generalization Comment 2 of 2 |
(In reply to Solution by Jer)

The relation of the solutions to the constant 4018 is not a coincidence:


Replace 4018 with 2C.

Proceeding as before the circle becomes

(y-C)^2 + (Z-C)^2 = 1

And the (x,y,z) system has solutions 
(1,C-1,C)
(1,C,C-1)
(-1,C+1,C)
(-1,C,C+1)

  Posted by Jer on 2015-06-19 07:09:09
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