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Given the square of 1+x+x +...+x to the 2010 power =0, find the value of x to the 2011 power Given the square of 1+x+x +...+x's 2010 power =0, find the value of x's 2011 power
1+X+x2+...+x^2010=0x+x2+x3+.+x^2010+x^2011=0.(1)1+x+x2+x3+.+x^2010=0x+x2+x3+.+x^2010=-1.(2) Substitute (2) into (1)-1+x^2011=0 so x^2011=1 Note: when x =-1,1+x...
Decomposition factor is used to prove that 257-512 can be divided by 120.
Certificate:257-512=(52)7-512
=514-512
=512×(52-1)
=512×24
=511×5×24
=511×120,
257-512 Can be divided by 120.
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