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Question Number 80974 by Rio Michael last updated on 08/Feb/20

Show that \gcd (a, a + x) ∣ x

h e n c e s h o w t h a t a n y t w o c o n s e c u t i v e

i n t e g e r s a r e c o p r i m e

Commented by kaivan.ahmadi last updated on 09/Feb/20

i f g c d (a, a + x) = d \Rightarrow d ∣ a \Rightarrow a = d y

a n d d ∣ a + x \Rightarrow a + x = d t

\Rightarrow d y + x = d t \Rightarrow x = d t - d y = d (t - y) \Rightarrow d ∣ x

Commented by Rio Michael last updated on 09/Feb/20

t h a n k s