Assuming that there's exactly one repeat (i.e., one number appears two times) in each row, which the for-loop solution also assumes, here's one way to do it without a loop:
a = [ 523 2920 523 1227
8003 8343 5611 8343
2066 5333 5333 5783
1447 2331 2331 8810
375 8083 8083 8343
5611 6866 5611 8343
2935 7026 5446 7026
1409 6842 6614 6842
2118 7208 4446 7208
4055 4439 4439 4921
42 8656 6691 8656
725 8478 822 8478
1003 1227 1227 6349
921 6614 6614 6842]
[m,n] = size(a);
[a_sorted,idx] = sort(a,2);
is_repeat = diff(a_sorted,1,2) == 0;
idx = idx.';
c = idx([is_repeat.'; false(1,m)]);
b = a(sub2ind([m n],(1:m).',c))
