Unique representation d = 4 k ( k 2 − 1 ) in D ( 4 ) - quadruples { k −
نویسنده
چکیده
Let k ≥ 3 be an integer. We show that if d is a positive integer such that the product of any two distinct elements of the set {k−2, k+2, 4k, d} increased by 4 is a square, then d must be 4k(k2−1).
منابع مشابه
On the family of Diophantine triples { k − 1 , k + 1 , 16 k 3 − 4 k }
It is proven that if k ≥ 2 is an integer and d is a positive integer such that the product of any two distinct elements of the set {k − 1, k + 1, 16k − 4k, d} increased by 1 is a perfect square, then d = 4k or d = 64k−48k+8k. Together with a recent result of Fujita, this shows that all Diophantine quadruples of the form {k − 1, k + 1, c, d} are regular.
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تاریخ انتشار 2006