a) 29=2²+5²
2²=4
5²=25
25-4=29
b) 29
2017
=29∗29
2016
=
=(25+4)*(29^{1008})^{2}==(25+4)∗(29
1008
)
2
=
=(5^{2}+2^{2})*(29^{1008})^{2}==(5
2
+2
2
)∗(29
1008
)
2
=
=5^{2}*(29^{1008})^{2}+2^{2}*(29^{1008})^{2}==5
2
∗(29
1008
)
2
+2
2
∗(29
1008
)
2
=
=(5*29^{1008})^{2}+(2*29^{1008})^2=(5∗29
1008
)
2
+(2∗29
1008
)
2
