Presupunem ca exista n²=4k+2
fie n∈{4m, 4m+1, 4m+2, 4m+3}, in functie de restul impartirii la 4
1. n=4m
=> n²=(4m)²=16m²=M4=4k
2. n=4m+1
=> n²=(4m+1)²=16m²+8m+1=M4+1=4k+1
3.n=4m+2
n²=(4m+2)²=16m²+16m+4=M4=4k
4. n=4m+3
=>n²=(4m+3)²=16m²+24m+9=4(4m²+6m+2)+1=M4+1=4k+1
=> n² poate avea forma 4k sau 4k+1
=> 4k+2 nu poate fi patrat perfect
