<s>[INST] If gcd$(a, 4) = 2$ and gcd$(b, 4) =2$, then gcd$(a + b, 4) = 4$ If gcd$(a, 4) = 2$ and gcd$(b, 4) =2$, then gcd$(a + b, 4) = 4$
can someone help me solve this.
 [/INST] $$\gcd(a, 4) = 2 \rightarrow a=4k+2\\\gcd(b, 4) = 2 \rightarrow b=4q+2\\\gcd(a+b, 4) = \gcd((4k+2+4q+2,4)=\gcd(4k+4q+4,4)\\\gcd(4(q+k+1),4)=4 $$
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