OFFSET
1,2
COMMENTS
For any prime p, there are finitely many k such that k^2+1 has p as its largest prime factor.
Numbers k such that k^2+1 is p-smooth appear in arctan-relations for the computation of Pi (for example, Machin's identity Pi/4 = 4*arctan(1/5) - arctan(1/239)), see the fxtbook link. [Joerg Arndt, Jul 02 2012]
LINKS
Joerg Arndt, Matters Computational (The Fxtbook), section 32.5 "Arctangent relations for Pi", pp. 633-640.
Filip Najman, Smooth values of some quadratic polynomials, Glasnik Matematicki Series III 45 (2010), pp. 347-355.
Florian Luca, Primitive divisors of Lucas sequences and prime factors of x^2 + 1 and x^4 + 1, Acta Academiae Paedagogicae Agriensis, Sectio Mathematicae 31 (2004), pp. 19-24.
Filip Najman, Home Page (gives all 811 numbers x such that x^2+1 has no prime factor greater than 197)
CROSSREFS
KEYWORD
nonn,hard,more
AUTHOR
Charles R Greathouse IV, Feb 21 2011
STATUS
approved