= Solution
Induct on the <Seifert genus> $g_s(K)$. A genus-zero knot is the <unknot>. If $K$ is prime there is nothing to prove. Otherwise write $K=K_1\mathbin{\#}K_2$ with both summands nontrivial. Part c gives
$$
g_s(K)=g_s(K_1)+g_s(K_2),
$$
so each summand has strictly smaller genus than $K$. Apply the induction hypothesis to both. Since the genus drops at every nontrivial split, the process terminates after finitely many steps and expresses $K$ as a finite <connected sum of knots>[connected sum] of <prime knot>[prime knots].
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