Question

1.Scrieti ca suma de patrate perfecte,distincte:
a)13
b)[tex] 13^{31}
c)65[/tex]
d)$45^{45}$

Answer 1

$a)13=9+4=3^{2}+2^{2}$
$b)13^{31}=13*13^{30}=(3^{2}+2^{2})*13^{30}=3^{2}*13^{30}+2^{2}*13^{30}=$
$3^{2}*(13^{15})^{2}+2^{2}*(13^{15})^{2}=(3*13^{15})^{2}+(2*13^{15})^{2}$
$c)65=64+1=8^{2}+1^{2}$
$d)45^{45}=45*45^{44}=(36+9)*45^{44}=(6^{2}+3^{2})*45^{44}=$
$6^{2}*45^{44}+3^{2}*45^{44}=6^{2}*(45^{22})^{2}+3^{2}*(45^{22})^{2}=$
$(6*45^{22})^{2}+(3*45^{22})^{2}$