An Absolute Bound for the Size of Diophantine m-Tuples

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On the size of Diophantine m-tuples (2000, unknown): “In [10] we proved that if n 6≡ 2 (mod 4) and n 6∈ {−4, −3, −1, 3, 5, 8, 12, 20}, then Mn ≥ 4. Recently, we were able to prove that M1 ≤ 8 (see [ 15 ]).”
There is no Diophantine quintuple (2016, background): “he Diophantine quintuple conjecture, Theorem 1, several researchers obtained several important results. Particularly, the ﬁrst absolute bound for the size of Diophantine m-tuples was given by Dujella [15], when he showed that m ≤ 8. In 2004, Dujella [16] proved that there does not exist a Diophantin”
The extensibility of Diophantine pairs {k−1,k+1} (2008, methodology): “As for (i), if v2m = w2n, then we know by Lemma 3(1) in [6] that z0 = z1.”
There are only finitely many Diophantine quintuples (2004, methodology): “In [9], Lemma 1, we proved the following lemma which describes the sets of solutions of the equations (4) and (5).”