AbstractBlade
New Member
- Joined
- Sep 8, 2020
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- 2021
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Induction
Damn beat me to it. The proof for whyInduction
(n+1)^5 + (n+1)^3 + 2(n+1)
= (n^5 + n^3 + 2n) + 4(n^4 + 2n^3 + 3n^2) + n^2 (n+1)^2 + 8n + 4
Alternatively, note that n(n+1) = 2(1+2+3+...+n)Damn beat me to it. The proof for whyis divisble by 4:
n is even: let n=2k then the expression becomes:
n is odd: let n=2k+1 then the expression becomes:![]()
More simply,Damn beat me to it. The proof for whyis divisble by 4:
n is even: let n=2k then the expression becomes:
n is odd: let n=2k+1 then the expression becomes:![]()
Wow just wow. Im interested on how thats derived?Black Magic Proof:
Observe the following identity:
All coefficients of the binomial sum are multiples of 4, and all binomial coefficients are integers, so the RHS is divisible by 4, hence the LHS must also be divisible by 4.
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use the greedy algorithm to successively eliminate the highest available power by subtracting the appropriately weighted binomial coefficientWow just wow. Im interested on how thats derived?