for any positive integer 'a' ,show that (2a+1,9a+4)=1.

Question

Elementry no. Theory- divisility theory for integer

Answer 1

(2a+1) for any value of a  The answer is odd number

(9a+4) for any value of a  The answer is odd number or even number 

2a+1<9a+1

If,a=0

then,(2a+1,9a+4)=1(gcd).

If,a=1,2,3,4,5,6,7,8,9 

then also (2a+1,9a+4)=1(gcd)

By maintaining this agrument For any valve upto 9 from 0 the ans is 1

Since,Both number cant be divisibe by 2,3,4,5,6,7,8,9; Then only G.C.D that left can be conclude from Previous result is 1

Since,(2a+1,9a+4)=1(gcd) <hence proved>                                                   For,Real +whole numbers