Friday, December 23, 2022

Prove that the polynomial $x^{9999} + x^{8888} + x^{7777} + ... + x^{1111} + 1$ $x^9999+x^8888+x^7777+...+x^1111+1$ is divisible by $x^{9} + x^{8} + x^{7} + ... . + x + 1$ $x^9+x^8+x^7+....+x+1$

Problem: 01

Prove that the polynomial

x^{9999} + x^{8888} + x^{7777} + ... + x^{1111} + 1

$x^9999+x^8888+x^7777+...+x^1111+1$ is divisible by

x^{9} + x^{8} + x^{7} + ... . + x + 1

$x^9+x^8+x^7+....+x+1$

Solution

Thursday, December 22, 2022

Find all function $f (x)$ $f(x)$ if $(x - y) f (x + y) - (x + y) f (x - y) = 4 x y (x^{2} - y^{2})$ $(x-y)f(x+y)-(x+y)f(x-y)=4xy(x^2-y^2)$

Find all function $f (x)$ $f(x)$ if $(x - y) f (x + y) - (x + y) f (x - y) = 4 x y (x^{2} - y^{2})$ $(x-y)f(x+y)-(x+y)f(x-y)=4xy(x^2-y^2)$

Solution

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