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Proving a Sum Identity for Variance Estimator

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#statistics #variance #estimation #sums-of-squares
186
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Sums of Squares algorithm

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#elementary-number-theory #sums-of-squares
96
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Is there another formula which generates Pythagoras' triples such that the largest $2$ of the triple differ by $3$?

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#algebra-precalculus #closed-form #sums-of-squares #pythagorean-triples
138
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Variance of the Square

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#statistics #normal-distribution #variance #sums-of-squares
74
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Is there a way to simplify $ \sum_{i=0}^k \cos^2\left(\frac{\pi}{2}+\left\lfloor\frac{n}{b^i}\right\rfloor \frac{2 \pi}{b}\right) $?

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#sequences-and-series #summation #sums-of-squares
431
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How to find the sum of squares of $1\ldots N-1$ that add to a squared number $N^2$?

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#sums-of-squares
88
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Equality on sum of squares constraint

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#optimization #convex-optimization #nonlinear-optimization #sums-of-squares #non-convex-optimization
107
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Distinct positive integers $x_1,x_2,x_3,x_4$ that satisfy $4x_1^2=x_2^2+2x_3^2+x_4^2.$

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#number-theory #diophantine-equations #sums-of-squares
132
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$\sigma(x,y,z)=xy+yz+zx$ and its connection to sums of squares

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#sums-of-squares #cyclic-decomposition
265
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Show that the sum of the squares of 3,4,5 and 6 consecutive numbers can not be a square

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#elementary-number-theory #modular-arithmetic #divisibility #sums-of-squares
51
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Properties of ordered pairs that satisfy $x^2 +y^2 =a$

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#square-numbers #sums-of-squares
202
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Products of sums of $2n$ squares

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#number-theory #square-numbers #sums-of-squares
150
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How many ways can an integer be written as a sum of three integer squares

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#combinatorics #number-theory #physics #sums-of-squares
88
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eucledian geometry

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#euclidean-geometry #ratio #sums-of-squares
210
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Characterizing integer solutions to $a^2 \mid \bigl((b^2)^2 + (b^2+1)^2\bigr)$

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#elementary-number-theory #divisibility #diophantine-equations #sums-of-squares

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