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2016 and Perfect Square Puzzle (Posted on 2016-06-22)

Determine all possible positive integer solutions to this system of equations:
A+B = 2016, and:
A²+B is a perfect square

See The Solution Submitted by K Sengupta

Rating: 5.0000 (1 votes)

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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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