prove that any integer n > 2 can be written in the form n = 2x + 3y where x, y > 0 are integers.
Follow Math Help Forum on Facebook and Google+
Originally Posted by bearej50 prove that any integer n > 2 can be written in the form n = 2x + 3y where x, y > 0 are integers. Think about the ways that you can express n as an even integer and as an odd integer. To start, for y = 0, n = 2x accounts for all even integers...
Prove by induction. Base Case is fairly easy. The inductive step is done in two parts. i) When x>0 (replace x by x-1 and y by y+1 and you have n+1) ii) When x=0 (replace y by y-1 and x by x+2 and you have n+1)
Originally Posted by bearej50 prove that any integer n > 2 can be written in the form n = 2x + 3y where x, y > 0 are integers. If is even then we can write . If is odd then is even and then .
View Tag Cloud