SOLUTION: Perfect Squares. Find a positive integer such that the integer increased by 1 is a perfect square and one-half of the integer increased by 1 is a perfect square. Also find the next

Question 129389This question is from textbook
: Perfect Squares. Find a positive integer such that the integer increased by 1 is a perfect square and one-half of the integer increased by 1 is a perfect square. Also find the next two larger positive integers that have this same property.
(this is what I put x^2+1+1/2x^2+1) This question is from textbook

Answer by 303795(602) (Show Source): You can put this solution on YOUR website!
First positive integer is 48.
(48+1) = 49 (ie 7 squared)
(48/2) = 24
(24+1) = 25 (ie 5 squared)
.
Next positive integer is 1680
(1680+1) = 1681 (ie 41 squared)
(1680/2) = 840
(840+1) = 841 (ie 29 squared)
.
Next positive integer is 57120
(57120+1) = 57121 (ie 239 squared)
(57120/2) = 28560
(28560+1) = 28561 (ie 169 squared)
.
Note if the condition that the integer had to be positive was not included then the first integer would be 0
(0+1) = 1 (ie 1 squared)
(0/2) = 0
(0+1) = 1 (ie 1 squared)
. Try also 1940448
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