OFFSET
1,2
REFERENCES
Richard K. Guy, Unsolved Problems in Number Theory, Springer-Verlag, 2004, ISBN 0-387-20860-7.
Carl Pomerance, Computational Number Theory, The Princeton Companion to Mathematics, Princeton University Press, 2008, pp. 361-362.
LINKS
Jordan Ellenberg, Mochizuki on ABC, Sep 03 2012.
Dorian Goldfeld, Beyond the last theorem, Math Horizons, 1996 (September), pp. 26-34.
Reken Mee met ABC, Synthese resultaten, (Dutch), 2011.
Wikipedia, abc conjecture
EXAMPLE
a(2) = 6 because there are 6 (a,b,c) triples with c < 10^2 and q > 1. Those triples are {1,8,9}, {1,48,49}, {1,63,64}, {1,80,81}, {5,27,32}, and {32,49,81}.
MATHEMATICA
rad[n_] := Times @@ Transpose[FactorInteger[n]][[1]]; Table[t = {}; mx = 10^n; Do[c = a + b; If[c < mx && GCD[a, b] == 1 && Log[c] > Log[rad[a*b*c]], AppendTo[t, {a, b, c}]], {a, mx/2}, {b, a, mx - a}]; Length[t], {n, 3}] (* T. D. Noe, Sep 06 2012 *)
CROSSREFS
KEYWORD
nonn,more
AUTHOR
Jonathan Vos Post, Sep 05 2012
STATUS
approved