When (1+x)ⁿ is expanded in ascending powers of x, N₁ of the coefficients leave a remainder of 1 when divided by 3, while N₂ of the coefficients leave a remainder of 2 when divided by 3. Prove that N₁-N₂=2^k where k is the number of 1's in the base 3 representation of n.

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Posted by Kyle Linel on 2024-10-01 09:20:43