3x+4y=3x+3y+y=3(x+y)+y
3x+4y=4x-x+4y=4(x+y)-x
Deci (3x+4y)=[tex] M_{3}+y= \frac{M}{4}-x [/tex]
Numerele de forma [tex] M_{3},~ M_{4}+2 ~si~ M_{4}+3 ~nu~pot~fi~patrate~perfecte =>[/tex] x∉{1,2,5,6,9} si y∉{2,5,8}.
Deci x∈{0,3,4,7,8}.
x=0 => y∈{0,1,4,9}
x=3 => y∈{0,4}
x=4 => y∈{1,6}
x=7 => y∈{1,7}
x=8 => y=3.
(x,y)∈{(0,0);(0,1);(0,4);(0,9);(3,0);(3,4);(4,1);(4,6);(7,1);(7,7);(8,3)}.
