A047210 Largest square modulo n.

0, 1, 1, 1, 4, 4, 4, 4, 7, 9, 9, 9, 12, 11, 10, 9, 16, 16, 17, 16, 18, 20, 18, 16, 24, 25, 25, 25, 28, 25, 28, 25, 31, 33, 30, 28, 36, 36, 36, 36, 40, 39, 41, 37, 40, 41, 42, 36, 46, 49, 49, 49, 52, 52, 49, 49, 55, 57, 57, 49, 60, 59, 58, 57, 64, 64, 65, 64, 64, 65, 64, 64, 72

Offset: 1

Author

Henry Bottomley, Jun 08 2000

Keywords

• easy
• nonn

Links

• T. D. Noe, Table of n, a(n) for n=1..1000
• Eric Weisstein's World of Mathematics, Quadratic Residue

Crossrefs

Last elements of rows of A096008.

Programs

Mathematica

Table[r=Range[n]; Max[Mod[r^2, n]], {n, 100}] (* T. D. Noe, Dec 18 2008 *)
Table[r = Range[1 + n/2]; Max[Mod[r^2, n]], {n, 100}] (* Zak Seidov, Dec 18 2008 *)

PARI

residue(n,m)={local(r);r=0;for(i=0,floor(m/2),if(i^2%m==n,r=1));r}
A047210(n)={local(r,m);r=0;m=n;while(r==0,m=m-1;if(residue(m,n),r=1));m} (End)