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A117986 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}. 2
1, 3, 4, 6, 6, 35, 8, 50, 20 (list; graph; refs; listen; history; text; internal format)
OFFSET

1,2

COMMENTS

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.

LINKS

Table of n, a(n) for n=1..9.

EXAMPLE

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.

CROSSREFS

Cf. A117987, A117988.

Sequence in context: A220345 A135510 A065967 * A248738 A070737 A225647

Adjacent sequences:  A117983 A117984 A117985 * A117987 A117988 A117989

KEYWORD

nonn,more

AUTHOR

John W. Layman, Apr 07 2006

STATUS

approved

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Last modified August 19 23:35 EDT 2017. Contains 290821 sequences.