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What is the remainder when x+x⁹+x²⁵+x⁴⁹+x⁸¹ is divided by x³-x ?

What is the remainder when x+x⁹+x²⁵+x⁴⁹+x⁸¹ is divided by x³-x ?

$x + x^{9} + x^{25} + x^{49} + x^{81} = x (1 + x^{8} + x^{24} + x^{48} + x^{80}) = x [(x^{80} - 1) + (x^{48} - 1) + (x^{24} - 1) + (x^{8} - 1) + 5] = x (x^{80} - 1) + x (x^{48} - 1) + x (x^{24} - 1) + x (x^{8} - 1) + 5 x n o w, x^{3} - x = x (x^{2} - 1) t h e r e f o r e, a l l t h e t e r m s b u t t h e l a s t t e r m 5 x a r e d i v i s i b l e b y x (x^{2} - 1) h e n c e, t h e r e m a i n d e r = 5 x .$

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