MathDB

For the several values of the parameter

m\in \mathbb{N^{*}}

,find the pairs of integers

(a,b)

that satisfy the relation

\ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \frac{[a,m]+[b,m]}{(a+b)m}=\frac{10}{11}

,
and,moreover,on the Cartesian plane

Oxy

the lie in the square

D=\{(x,y):1\leq x\leq 36,1\leq y\leq 36\}

.
Note:

[k,l]

denotes the least common multiple of the positive integers

k,l

Problem Statement