gcd

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

8 Answers

·

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.

21
Arnab Kundu ·

thank you

21
Shubhodip ·

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

by bezout's theorem gcd is 1

21
Arnab Kundu ·

thik i toh!!

1
sanchit ·

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

1
chinmaya ·

gcd=hcf[1]

1
sanchit ·

ooh kk silly of me!!!!!!

1
Arkodip Mandal ·

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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