ABCExceptions

5 Bibliography

1

T.F. Bloom and J.D. Lichtman, The Bombieri-Pila determinant method. Preprint, 2023. (arXiv:2312.12890)

2

E. Bombieri and J. Pila, The number of integral points on arcs and ovals. Duke Math. J. 59 (1989), 337–357.

3

E. Bombieri and W.M. Schmidt, On Thue’s equation. Invent. Math. 88 (1987), 69–81.

4

N.G. de Bruijn, On the number of integers \(\leq x\) whose prime factors divide \(n\). Illinois J. Math. 6 (1962), 137–141.

5

H. Darmon and A. Granville, On the equations \(z^m=F(x,y)\) and \(Ax^p+By^q=Cz^r\). Bull. London Math. Soc. 27 (1995), 513–543.

6

D.R. Heath-Brown, Diophantine approximation with square-free numbers. Math. Zeit. 187 (1984), 335–344.

7

D.R. Heath-Brown, The density of rational points on cubic surfaces. Acta Arith. 79 (1997), 17–30.

8

D.R. Heath-Brown, Counting rational points on algebraic varieties. Analytic number theory, 51–95, Lecture Notes in Math. 1891, Springer-Verlag, 2006.

9

D. Kane, On the number of ABC solutions with restricted radical sizes. J. Number Theory 154 (2015), 32–43.

10

B. Mazur, Questions about powers of numbers. Notices Amer. Math. Soc. 47 (2000), 195–202.

11

H. Pasten, The largest prime factor of \(n^2+1\) and improvements on subexponential ABC. Invent. Math. 236 (2024), 373–385.

12

C.L. Stewart and K.R. Yu, On the \(abc\) conjecture. II. Duke Math. J. 108 (2001), 169–181.