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Searching for Diophantine quintuples

100%

Cipu M., Trudgian T.

Acta Arithmetica

2016

tom 173

nr 4

365-382

We consider Diophantine quintuples {a, b, c, d, e}. These are sets of positive integers, the product of any two elements of which is one less than a perfect square. It is conjectured that there are no Diophantine quintuples; we improve on current estimates to show that there are at most $5.441·10^{26}$ Diophantine quintuples.

On Grosswald's conjecture on primitive roots

81%

Cohen S., Oliveira e Silva T., Trudgian T.

Acta Arithmetica

2016

tom 172

nr 3

263-270

Grosswald's conjecture is that g(p), the least primitive root modulo p, satisfies g(p) ≤ √p - 2 for all p > 409. We make progress towards this conjecture by proving that g(p) ≤ √p -2 for all $409 < p < 2.5 × 10^{15}$ and for all $p > 3.38 × 10^{71}$.

Ograniczanie wyników

2 Acta Arithmetica

2 Trudgian T.

1 Cipu M.

1 Cohen S.

1 Oliveira e Silva T.

2 2016

Wyniki wyszukiwania

Searching for Diophantine quintuples

On Grosswald's conjecture on primitive roots