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2016 and Perfect Square Puzzle (Posted on 2016-06-22) Difficulty: 3 of 5
Determine all possible positive integer solutions to this system of equations:
A+B = 2016, and:
A2+B is a perfect square

No Solution Yet Submitted by K Sengupta    
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Man way | Comment 2 of 4 |
B=2016-A
A^2+2016-A=C^2
A=(1+-sqrt (4C^2-8063))/2  [1]

4C^2-8063 is square if 8063=4Cn-n^2=n(4C-n)
As 8063=733*11 (both primes)
Or n=11 and 4C-n=733 =>C=186
Or n=733 and 4C-n=11 =>C=186

Then  from [1]  A=(1+-361)/2  A=181 and -180
B=1835 and 2196

We are asked for positive integers. 
Anyway there is a solution also con A negative
So:
 181+1835=2016  181^2+1835=186^2
(-180)+2196=2016  (-180)^2+2196=186^2

Edited on June 22, 2016, 5:11 pm
  Posted by armando on 2016-06-22 17:08:37

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