give-a-Z-and-prove-that-if-a-2-4-than-a-3-can-t-6-

Question Number 116513 by bounhome last updated on 04/Oct/20

g i v e a \in Z a n d p r o v e t h a t i f (a - 2) ∣ 4 t h a n (a - 3) {c a n}^{'} t ∣ 6

Answered by floor(10²Eta[1]) last updated on 04/Oct/20

a - 2 ∣ 4 \Rightarrow a - 2 \in {\pm 1, \pm 2, \pm 4}

\Rightarrow a \in A : {- 2, 0, 1, 3, 4, 6}

a - 3 ∣ 6 \Rightarrow a - 3 \in {\pm 1, \pm 2, \pm 3, \pm 6}

\Rightarrow a \in B : {- 3, 0, 1, 2, 4, 5, 6, 9}

A \cap B = C : {0, 1, 4, 6}

so a - 2 ∣ 4 and a - 3 ∣ 6 if and only if a \in C