Re: HSC 2013 3U Marathon Thread
= (x^32-1)/(x-1)
= (x^16-1)(x^16+1)/(x-1)
= (x^8-1)(x^8+1)(x^16+1)/(x-1)
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= (x-1)(x+1)(x^2+1)(x^4+1)(x^8+1)(x^16+1)/(x-1)
= (x+1)(x^2+1)(x^4+1)(x^8+1)(x^16+1)
= LHS
RHS = 1 + x + x^2 + ... + x^31
= (x^32-1)/(x-1)
= (x^16-1)(x^16+1)/(x-1)
= (x^8-1)(x^8+1)(x^16+1)/(x-1)
.
.
.
.
= (x-1)(x+1)(x^2+1)(x^4+1)(x^8+1)(x^16+1)/(x-1)
= (x+1)(x^2+1)(x^4+1)(x^8+1)(x^16+1)
= LHS