010: Sum / Sums of Three Cubes, Part 1 · Chapter 6: Third Powers.

005b: Sums of n squares · Note 2: For what n is the square of n squares identically the sum of · A. Boutin · Boutin's Identity · where the exterior sign is the ...

010: Sum / Sums of Three Cubes, Part 1 · 011: Sum / Sums of Three Cubes, Part 2 · 012: Cubic Polynomial as a kth Power · 013: Sum / Sums of two Fourth Powers.

010: Sum / Sums of Three Cubes, Part 1 · 011: Sum / Sums of Three Cubes ... sum of four squares by Euler's Four-Square Identity. The case n = 3 shows ...

003: Sum / Sums of two squares ... where {x 1, x 2, x 3} = {4(x+2y-2z)(x-y-z), x 2-8xy-2y 2+12yz-2z 2, 3x 2+6y 2-8xz-4yz+6z 2}. The advantage of the first method ...

010: Sum / Sums of Three Cubes, Part 1 · 011: Sum / Sums of Three Cubes, Part 2 · 012: Cubic Polynomial as a kth Power · 013: Sum / Sums of two Fourth Powers.

1. Form: x 2+y 2+z 2 = t k. Geometrically, the case k = 2 of Form 1 can be seen as a cuboid with sides {x,y,z} and space diagonal t, · 2. Form: x 2+y 2+z 2 = u ...

010: Sum / Sums of Three Cubes, Part 1 · 011: Sum / Sums of Three Cubes, Part 2 · 012: Cubic Polynomial as a kth Power · 013: Sum / Sums of two Fourth Powers.

001c: Assorted Identities, Part 3 (Equal Sums of Like Powers) · 0020 ... 010: Sum / Sums of Three Cubes, Part 1 · 011: Sum / Sums of Three Cubes, Part ...

Sum / Sums of biquadrates (This page covers eqs 1-9.) a 4+b 4 = c 4 ...

010: Sum / Sums of Three Cubes, Part 1 · 011: Sum / Sums of Three Cubes, Part 2 · 012: Cubic Polynomial as a kth Power · 013: Sum / Sums of two Fourth Powers.

or the sum of two consecutive cubes. (The sum of two consecutive squares will appear in the next section.) Apery would later give a similar formula,. where ...

This has recurrence relation F(n) = F(n-1) + F(n-2), or each term is the sum of the previous two, and φ is its limiting ratio (also for the Lucas numbers, a ...

010: Sum / Sums of Three Cubes, Part 1 · 011: Sum / Sums of Three Cubes, Part 2 · 012: Cubic Polynomial as a kth Power · 013: Sum / Sums of two Fourth Powers.

010: Sum / Sums of Three Cubes, Part 1 · 011: Sum / Sums of Three Cubes, Part 2 · 012: Cubic Polynomial as a kth Power · 013: Sum / Sums of two Fourth Powers.

010: Sum / Sums of Three Cubes, Part 1 · 011: Sum / Sums of Three Cubes ... Difference of Two Squares Identity. Part 3. Quadratic Polynomial as a kth ...

010: Sum / Sums of Three Cubes, Part 1 · 011: Sum / Sums of Three Cubes, Part ... summation, easily done by computer algebra systems like Mathematica.

010: Sum / Sums of Three Cubes, Part 1 · 011: Sum / Sums of Three Cubes, Part 2 · 012: Cubic Polynomial as a kth Power · 013: Sum / Sums of two Fourth Powers.

010: Sum / Sums of Three Cubes, Part 1 · 011: Sum / Sums of Three Cubes, Part ... into a sum and difference of any number of biquadrates and apply it to the ...

Voronoi summation formula for a generalized divisor function, ... Perfect powers in alternating sum of consecutive cubes,. Glasnik Mathematicki ...