Question

What is the minimum value of abs(187m-396n-526
) as m,n take all integer values?

Answer 1

answer : 2

we have to find minimum value of abs(187m - 396n - 526) where m and n are integers.

prime factors of 187 = 11 × 17

prime factors of 396 = 2 × 2 × 3 × 3 × 11

= 11 × 36

so, (187m - 396n - 526) can be written as 11(17m - 36n) - 526

because m and n are integers .

so, (17m - 36n) also will be integers for all value of m and n.

let (17m - 36n) = P

then, 11P - 526

so, we have to find minimum value of abs(11P - 526)

take 11P = 526 => P = 526/11 = 47.8 ,

so, take P = 48

then, abs(11p - 526) = 11 × 48 - 526 = 2

hence, minimum value of abs(187m - 396n - 526) = 2.

Answer 2

Answer:

answer is 2

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