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Fix $k \ge 3$. If a multiplicative function $f$ satisfies \[ f(x_1+x_2+\dots+x_k) = f(x_1) + f(x_2) + \dots + f(x_k) \] for arbitrary positive triangular numbers $x_1, x_2, \dots, x_k$, then $f$ is the identity function. This extends Chung and Phong's work for $k=2$.
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참고문헌 (6)
참고문헌 신청
P. V. Chung / 1996 / Multiplicative functions satisfying the equation f(m2+n 2)= f(m2)+f(n 2) / Math. Slovaca 46(2-3):165~171
P. V. Chung / 1999 / Additive uniqueness sets for multiplicative functions / Publ. Math. Debrecen 55(3-4):237~243
Artūras Dubickas / 2013 / On multiplicative functions which are additive on sums of primes / Aequationes mathematicae 86(1-2):81~89
Jin-Hui Fang / 2011 / A characterization of the identity function with equation f(p+q+r)=f(p)+f(q)+f(r) / Combinatorica 31(6):697~701
Poo-Sung Park / 2018 / On k-additive uniqueness of the set of squares for multiplicative functions / Aequationes mathematicae 92(3):487~495
P. V. Chung / 1999 / Additive uniqueness sets for multiplicative functions / Publ. Math. Debrecen 55(3-4):237~243
Artūras Dubickas / 2013 / On multiplicative functions which are additive on sums of primes / Aequationes mathematicae 86(1-2):81~89
Jin-Hui Fang / 2011 / A characterization of the identity function with equation f(p+q+r)=f(p)+f(q)+f(r) / Combinatorica 31(6):697~701
Poo-Sung Park / 2018 / On k-additive uniqueness of the set of squares for multiplicative functions / Aequationes mathematicae 92(3):487~495
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