A109760 Composite n such that binomial(5*n,n) == 5^n (mod n).

4, 365, 400, 685, 3200, 6400, 12550, 12800, 16525, 25600, 51200, 225125, 70463125, 271094125, 431434441

Offset: 1

Author

Ryan Propper, Aug 12 2005

Keywords

• hard
• more
• nonn

Comments

No other terms below 10^9.

Examples

			4 is a term because binomial(5*4, 4) = 4845, 5^4 = 625 and 4845 mod 4 = 625 mod 4 = 1.
		

Links

• Max Alekseyev, PARI/GP scripts for various problems

Crossrefs

Cf. A080469.

Programs

Mathematica

Do[If[ !PrimeQ[n], If[Mod[Binomial[5*n, n], n] == Mod[5^n, n], Print[n]]], {n, 1, 50000}]
Select[Range[250000],CompositeQ[#]&&Mod[Binomial[5#,#],#]==PowerMod[5,#,#]&] (* The program generates the first 12 terms of the sequence. *) (* Harvey P. Dale, Jul 28 2025 *)

Extensions

a(12) from D. S. McNeil, Mar 15 2009

225125 from Max Alekseyev, Sep 13 2009

Three more terms from Max Alekseyev, Nov 06 2009