Question

___________________________(/). State one reason for your selection.

Answer 1

Answer:

Give me One reason why you selected this.

Answer 2

Explanation:

Let f(m,n) = 45*m + 36*n, where m and n are integers (positive or negative). What is the minimum positive value for f(m,n) for all values of m and n (this may be achieved for various values of m and n)?

4 Questions and Answers



Krishna just, enthusiastic in searching for patterns

Answered 5 years ago · Author has 93 answers and 248.6K answer views

Let f(m,n) = 45*m + 36*n, where m and n are integers (positive or negative). What is the minimum positive value for f(m,n) for all values of m and n (this may be achieved for various values of m and n)?

Answer is 9

Explanation:

From Bézout's identity

The greatest common divisor (gcd) of non-zero integers a and b is the smallest positive integer that can be written as ax+byax+by (with x,yx,y as integers).

So now, the smallest positive value(say d), that can be written as 45m+36n45m+36n is the greatest common divisor of 45 and 36.

⟹d=gcd(45,36)⟹d=gcd(45,36)

⟹d=gcd(32∗5,22∗32)⟹d=gcd(32∗5,22∗32)

⟹d=32⟹d=32

⟹d=9⟹d=9

Therefore, the minimum positive value for f(m,n)f(m,n) for all integer values of m,nm,n is equal to 9.