A121278 Number of distinct integers of the form (x^n + y^n) mod n^2.

1, 3, 5, 3, 13, 9, 19, 5, 15, 15, 51, 9, 73, 30, 65, 9, 113, 21, 163, 9, 25, 63, 265, 15, 65, 57, 45, 30, 281, 45, 391, 17, 255, 123, 247, 21, 577, 165, 65, 15, 841, 27, 757, 63, 195, 234, 1105, 27, 133, 75, 565, 30, 1249, 57, 65, 50, 95, 339, 929, 27, 1321, 408, 75, 33, 949

Offset: 1

Author

Max Alekseyev, Aug 23 2006

Keywords

• nonn

Comments

It is enough to take x,y from {0,1,...,n-1}. Therefore a(n)<=n*(n+1)/2.

Programs

PARI

{ a(n) = my(S, t); S=Set(); for(x=0,n-1, for(y=x,n-1, t=lift(Mod(x,n^2)^n+Mod(y,n^2)^n); S=setunion(S,[t]); ); ); #S }

PARI

a(n) = #setbinop((x, y)->Mod(x, n^2)^n+Mod(y, n^2)^n, [0..n-1]); \\ Michel Marcus, Oct 16 2023

Extensions

More terms from Michel Marcus, Oct 16 2023