mathematical optimization - What is wrong with my ArgMin expression?

I need to find the minimum of a function $mj_1^2+mj_2^2$ where my $mj$ are constrained.

I wrote this expression:

ArgMin[
  {mj1^2 + mj2^2, mj1 == (M1 + 1)*p1, p1 ∈ Integers, 
   mj2 == (M2 + 1)*p2, p2 ∈ Integers, 
   MemberQ[{mj1, mj2} , couplesm]}, {mj1, mj2}]

Indeed, my mj's must be multiples of Mj + 1, and they musn't be part of a list given by couplesm.

When I evaluate it, I get the following message;

ArgMin::infeas: There are no values of {mj1, mj2} for which the constraints False are satisfied and the objective function mj1^2 + mj2^2 is real valued.

I even added p1 and p2 to the variables of minimization, but it still didn't work.

How can I find the minimum of: $mj_1^2+mj_2^2$, where $mj_i$ is a multiple of $M_i+1$ and where the pairs $(mj_1,mj_2)$ can't be inside of the list couplesm?

Edit

I wrote the following and the code still doesn't work.

couplesm = {{0, 0}}

{{0, 0}}

ArgMin[

  {mj1^2 + mj2^2, 
   IntegerQ[mj1/(M1 + 1)], IntegerQ[mj2/(M1 + 1)], 
   mj1 ∈ Integers, mj2 ∈ Integers, 
   Sequence @@ Table[{mj1, mj2} != couplesm[[i]], {i, 1, Length[couplesm]}]}, 
  {mj1, mj2}]

ArgMin::infeas: There are no values of {mj1,mj2} for which the constraints False are satisfied and the objective function mj1^2+mj2^2 is real valued.

{Indeterminate, Indeterminate}