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arXiv · 2603.29565

On Diophantine pairs and triples of triangular numbers

Marija Bliznac Trebješanin
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Abstract

We investigate Diophantine pairs and triples of triangular numbers with the property $D(a)$ for a non-zero integer $a$. We prove that if a triangular number belongs to a $D(a)$-pair, it can be extended to infinitely many $D(a)$-triples of triangular numbers. Additionally, we determine infinite families of integers $a$ that admit such pairs, as well as families for which no $D(a)$-pairs can exist.

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Marija Bliznac Trebješanin. 2026-06-18. On Diophantine pairs and triples of triangular numbers. https://arxiv.org/abs/2603.29565

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