We use cookies to personalise content and advertisements and to analyse access to our website. Furthermore, our partners for online advertising receive pseudonymised information about your use of our website.
Please click on "Accept cookies" if you agree to the setting of cookies. Cookies that do not require consent remain unaffected by this, see
cookie policy and privacy policy.
DECLINE COOKIES

Find the ordered pair $(m,n),$ where $m,n$ are positive integers satisfying the following equation: $$6mn = 27 - 3m - 2n$$

gueesstt Apr 22, 2018

#1**+1 **

6mn = 27 - 3m - 2n add 2n to both sides

6mn + 2n = 27 - 3m factor this

2n ( 3 + m) = 3(9 - m)

Because of "2n"....the left side is always even

And the right side will be even when "m" is odd

Divide both sides by 3

(2/3)n (3 + m) = 9 - m

The right side is an integer

The left side will be an integer when "n" is a multiple of 3

Note that when n = 3 and m = 1, we have that

(2/3)(3)(3 + 1) = 9 - 1

2(3 + 1) = 9 - 1

2(4) = 8 which is true

So....(m, n) = (1, 3)

CPhill Apr 22, 2018