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

Show that gcd (a , a + x) ∣ x hence show that any two consecutive integers are coprime

Showthatgcd(a,a+x)∣xhenceshowthatanytwoconsecutiveintegersarecoprime

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

if gcd(a,a+x)=d⇒d∣a⇒a=dy and d∣a+x⇒a+x=dt ⇒dy+x=dt⇒x=dt−dy=d(t−y)⇒d∣x

ifgcd(a,a+x)=d⇒d∣a⇒a=dyandd∣a+x⇒a+x=dt⇒dy+x=dt⇒x=dt−dy=d(t−y)⇒d∣x

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

thanks

thanks

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