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Scrieti numarul [tex] 314^{2017} [/tex] ca o suma de 5 patrate perfecte.(demonstratie)Dau coroana

Răspuns :

314^2017 =

= 314^2016 × 314 =

= 314^2016 × ( 2^2 + 3^2 + 6^2 + 11^2 + 12^2) =

= (314 × 2)^2 + (314 × 3)^2 + (314 × 6)^2 +

(314 × 11)^2 + (314 × 12)^2



314 = 4 + 9 + 36 + 121 + 144