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Find additional pairs (Posted on 2016-08-08) Difficulty: 3 of 5
The pair of positive integers (4,6) satisfies the equation

(2x+1)*x=y^2

Find at least three additional pairs, both x and y below 10^6.

See The Solution Submitted by Ady TZIDON    
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General solution Comment 5 of 5 |

0 0
-1 -1
4 6
-25 -35
144 204
-841 -1189
4900 6930
-28561 -40391
166464 235416
-970225 -1372105
5654884 7997214
-32959081 -46611179
192099600 271669860
-1119638521 -1583407981
6525731524 9228778026
-38034750625 -53789260175

Succeeding positive terms obey the recurrence a(n+1) = INT (1+2^(1/2))^4*a(n), or even a(n+1) = INT a(n)^2/a(n-1)

Edited on August 9, 2016, 7:26 am
  Posted by broll on 2016-08-09 07:18:39

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