query: Proving the sum of cubes?
positive_passages.docid: 15100
positive_passages.text: Proving the identity $\sum_{k=1}^n {k^3} = \big(\sum_{k=1}^n k\big)^2$ without induction
negative_passages.docid: 32260
negative_passages.text: Alternating Sum of Cubes
negative_passages.docid: 4194
negative_passages.text: Which integers can be expressed as a sum of squares of two coprime integers?
negative_passages.docid: 49928
negative_passages.text: Proving limit of a sum
negative_passages.docid: 41789
negative_passages.text: Fermat's theorem on sums of two squares
negative_passages.docid: 87666
negative_passages.text: Find $n$ such that $n/2$ is a square, $n/3$ is a cube, and $n/5$ a fifth power
negative_passages.docid: 30338
negative_passages.text: How to prove that $\sum_{k=0}^n \binom nk k^2=2^{n-2}(n^2+n)$
negative_passages.docid: 90904
negative_passages.text: Combinatorial proof of an identity with squared binomial coefficients
negative_passages.docid: 16472
negative_passages.text: Sum of First $n$ Squares Equals $\frac{n(n+1)(2n+1)}{6}$
negative_passages.docid: 107395
negative_passages.text: If the sum of $n$ cubes is zero, then the sum must be no larger than $\frac n3$.
negative_passages.docid: 92106
negative_passages.text: Prove that $n$ is a sum of two squares?
negative_passages.docid: 103146
negative_passages.text: Proof that the Rubik’s Cube group is 2-generated
negative_passages.docid: 143374
negative_passages.text: Elegant proof that maximum of sums is, at most, sum of maximums
negative_passages.docid: 114277
negative_passages.text: Proving in Discrete Structures Problem that $2^N = \binom{N}{0} + \binom{N}{1} + \binom{N}{2} + \dots + \binom{N}{N}$
negative_passages.docid: 156577
negative_passages.text: The cube of any number not a multiple of $7$, will equal one more or one less than a multiple of $7$
negative_passages.docid: 66216
negative_passages.text: Squares, Cubes and Prime numbers
negative_passages.docid: 62747
negative_passages.text: Use induction to prove a product of sums of squares is a sum of squares