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An interesting proof of polynomial

Prove that x^3m+x^3k+1+x^3n+2 is divisible by x^2+x+1 such that m,k,n are any non -negative integers.

Note by Sayantan Nandy
3 years, 11 months ago

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P(x) is divisible by x-a if P(a)=0. Factor theorem. So, x2+x+1 has two roots -1/2+isqrt(3)/2 and -1/2-isqrt(3)/2 If P(x) is your above polynomial. P(-1/2+isqrt(3)/2)=0 and P(-1/2-isqrt(3)/2)=0. So your polynomial x^3m+x^3k+1+x^3n+2 is divisible by x^2+x+1.

Balaji Dodda - 3 years, 11 months ago

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