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%I #9 Sep 19 2019 19:11:17
%S 1,3,4,6,6,35,8,50,20,55,12,160,14,75,160,194,18,195,20,256,220,115,
%T 24,3936,102,135,164,352,30,5301,32,770,340,175,352,2496,38,195,400,
%U 6396,42,7353,44,544,928,235,48,15456,296,1015,520,640,54,1635,544,8856
%N Number of functions f:[n]->[n] such that f[(x*y) mod n]=[f(x)*f(y)] mod n for all x,y in [n], for n=1,2,3,... Here [n] denotes {0,1,2,...,n-1}.
%C 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.
%H Rémy Sigrist, <a href="/A117986/a117986.txt">C++ program for A117986</a>
%F Apparently, a(p) = p + 1 for any prime number p. - _Rémy Sigrist_, Sep 19 2019
%e 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.
%o (C++) See Links section.
%Y Cf. A117987, A117988.
%K nonn
%O 1,2
%A _John W. Layman_, Apr 07 2006
%E More terms from _Rémy Sigrist_, Sep 19 2019
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