integer pair search

[Doegon]

guys i'm to write an application program that gets a filename and number form the command line and print all possible pairs of numbers such that a<b< number and (a^2 +b^2 +1)/ab is an integer

e.g number = 1000
filename = integers.txt

output is
(1,2)
(2,5)
(5,13)
(13,34)
(34,89)
(89,233)
(233,610)

from this example the integer is always three.but the problem is i can't come with an algorith to produce the output.you help will be much appreciated guys

[chaarmann]

a very simple method is to just loop through each value a=1,2,3,... and b=1,2,3,... and compute the value by given formula. Then see if the result is an integer by comparing

boolean isInteger = (Math.round(result) == result);.

Or, to avoid float numbers at all,you could calculate

 int x= (a * a + b * b +1);
int y = a * b;
boolean isInteger = (x % y == 0); 

guys i'm to write an application program that gets a filename and number form the command line and print all possible pairs of numbers such that a<b< number and (a^2 +b^2 +1)/ab is an integer

e.g number = 1000
filename = integers.txt

output is
(1,2)
(2,5)
(5,13)
(13,34)
(34,89)
(89,233)
(233,610)

from this example the integer is always three.but the problem is i can't come with an algorith to produce the output.you help will be much appreciated guys