Multiplicative functions with f(p+q-n0) = f(p)+f(q)-f(n0)
Abstract
Let n0 be 1 or 3. If a multiplicative function f satisfies f(p+q-n0) = f(p)+f(q)-f(n0) for all primes p and q, then f is the identity function f(n)=n or a constant function f(n)=1.
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Let n0 be 1 or 3. If a multiplicative function f satisfies f(p+q-n0) = f(p)+f(q)-f(n0) for all primes p and q, then f is the identity function f(n)=n or a constant function f(n)=1.