1,2

If, instead, the modular functional equation f[(x+y) mod n]=[f(x)+f(y)] mod n is considered, it is found that for each n=1,2,3,... there appears to be exactly n functions with the desired property. See A117987 and A117988 for results on other modular functional equations.

For n=5 the six functions are (0,0,0,0,0), (0,1,1,1,1), (1,1,1,1,1), (0,1,4,4,1),

(0,1,3,2,4), (0,1,2,3,4). For the 5th of these, (0,1,3,2,4), the x=2, y=3 case is verified by the calculations f(2*3 mod 4)= f(1)=1 and f(2)*f(3) mod 5=3*2 mod 5=1.

Cf. A117987, A117988.

Adjacent sequences: A117983 A117984 A117985 this_sequence A117987 A117988 A117989

Sequence in context: A133689 A135510 A065967 this_sequence A070737 A135599 A129000

nonn

John W. Layman (layman(AT)math.vt.edu), Apr 07 2006