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how can I prove that for every integer $a$ results gcd ($a$, $a$ + 7) = gcd ($a$, 7) ?

sickdamn
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    If $x$ divides $a$ and $a+7$ then it divides their difference. On the other hand if $x$ divides $a$ and $7$ then it divides their sum. – Asinomás Jan 23 '22 at 10:54
  • thanks for the answer, is right but I would need an exam proof to prove that proposition. – sickdamn Jan 23 '22 at 11:08
  • If $\frac ax$ and $\frac {a+7}x$ are integers, what can you say about $\frac {a+7}x-\frac ax$? – PM 2Ring Jan 23 '22 at 11:14
  • that are integers, but it doesn't answer the question that the gcd is the same, I mean. – sickdamn Jan 23 '22 at 11:19

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