1. Theorem. Let n, d, k ∈N a t, with 0

Question

1. Theorem. Let n, d, k ∈N a t, with 0<d, k. Then rem(k n, k d)=k(rem(n, d)) .  2. Theorem. Let

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For the first theorem, we want to prove that the remainder of $kn$ divided by $kd$ is equal to $

1. Theorem. Let $n, d, k \in N a t$, with $0<d, k$. Then $$ \operatorname{rem}(k n, k d)=k(\operatorname{rem}(n, d)) \text {. } $$ 2. Theorem. Let $n, m, k \in N a t$, with $0<k$. Then $$ \operatorname{gcd}(k n, k m)=k(\operatorname{gcd}(n, m)) \text {. } $$