gcd

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how can we prove gcd(n,n+1)=1

#Mathematics #Class VII-X Mathematics

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8 Answers

·2011-05-31 21:49:53

let the gcd be d.
d divides n as well as n+1.
also divides their difference i.e 1
hence if d|1 then d must be 1.

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21

Arnab Kundu ·2011-05-31 22:30:35

thank you

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Shubhodip ·2011-05-31 22:33:19

1(n+1) + (-1)n = 1

by bezout's theorem gcd is 1

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Arnab Kundu ·2011-05-31 22:51:52

thik i toh!!

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sanchit ·2011-05-31 23:54:52

which topic is this nd wht is thtis g c d????????:O

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chinmaya ·2011-05-31 23:59:41

gcd=hcf[1]

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sanchit ·2011-06-01 00:18:48

ooh kk silly of me!!!!!!

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Arkodip Mandal ·2013-05-17 23:57:44

gcd(n,1)=1
by bezout's theorum,
nu+1*v=1
or,nu+v+nv-nv=1
or,(n+1)*v + n(u-v)=1.

now ,
v and (u-v) are integers
so, gcd(n+1,n)=1.

hope that helps ..................

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