Let n be a positive odd integer, prove gcd(3n, 3n+16) = 1.
since n is odd so all factors of 3n are odd
but 16 is an even no. whose only prime factor is 2
let a be a common factor to both 3n and 3n+16
since a is one of the factor of 3n so , a divides 3n
or ,3n=ak for some integer k
also 3n+16 is divisible by a so ,
3n+16=am for some integer m
this implies 16 is divisible by a
but a is an odd number
so ,here is the contradiction
therefore 3n and 3n+16 has no common factor
PLEASE LIKE IT RAISE YOUR THUMBS UP
IF YOU ARE HAVING ANY DOUBT FEEL FREE TO ASK IN COMMENT SECTION
Get Answers For Free
Most questions answered within 1 hours.