Question

Va rog sa ma ajutati cu aceasta problema: Scrieti numarul 314 la puterea 2017 ca suma de 5 patrate perfecte!

Answer 1

314^2016*(314)=(289+25+0+0+0)*(314^1008)²=
=(17*314^1008)²+(5*314^1008)²+0²+0²+0²
suma de 5 patrate perfecte
nu ai zis nenule , nici diferite


altfel;NENULE si DIFERITEoricare 2 intre ele
314=169+145=169+100+45=169+100+25+16+4=13²+10²+5²+4²+2²

314*314^2016=(13²+10²+5²+4²+2²)*(314^1008)²=
=(314^1008*13)²+(10*314^1008)²+(5*314^1008)²+(4*314^1008)²+(2*314^1008)²
suma de 5 patrate perfecte

Answer 2

314^2017=314^2016x314=
=(314^1008)^2x2(2^2+5^2+8^2+10^2+11^2)=
=(314^1008x2)^2+(314^1008x5)^2+(314^1008x8)^2+(314^1008x10)^2+(314^1008x11)^2