Unfinished Business
Consider the set of solutions, in positive integers x, of 5x^2 + 2x + 1 = n, where n is a perfect square.
Show that if a and b are two solutions, with a < b, then 7b-2a+1 is also a solution.
Show that if a and b are two consecutive solutions (w/ no other solutions between them), then b and 7b-2a+1 are consecutive solutions.
I ran across this while programming, and know for a fact that the properties are true for at least the first (lowest) 15 solutions of x. I just can't figure out why...
Show that if a and b are two solutions, with a < b, then 7b-2a+1 is also a solution.
Show that if a and b are two consecutive solutions (w/ no other solutions between them), then b and 7b-2a+1 are consecutive solutions.
I ran across this while programming, and know for a fact that the properties are true for at least the first (lowest) 15 solutions of x. I just can't figure out why...