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Challenge 317: Is u an integer?
What values of x will mean that u is an integer?
Suppose that x2 + x + 1 = u2, where x is an integer.
Show that (2u)2 – 3 must be a perfect square, and hence find all the values of x for which u is also an integer.
What values of x will mean that u is an integer?
Suppose that x2 + x + 1 = u2, where x is an integer.
Show that (2u)2 – 3 must be a perfect square, and hence find all the values of x for which u is also an integer.