Mathematics Stack Exchange
Mathematics Stack Exchange

Questions tagged [sums-of-squares]

For questions concerning various representation of integers as sums of squares, which are studied in number theory.

For questions concerning various representation of integers as sums of squares, which are studied in number theory.

These topics include, for example:

737 questions
0
votes
0 answers

Sum of squares of a normalized sequence

Let a sequence $X = \{x_1, x_2, ..., x_n\}$ and $n = k \times l$ in which $k,l \in \mathbb{N}$. We have the following conditions: $$A)\sum_{i=1}^{n} x_i = 0$$ $$B)\sum_{i=1}^{n} x_i^2 = 1$$ I was wondering if we could convert the following…
Patris
  • 11
  • 1
0
votes
1 answer

How to show that sum of squares is n times of mean?

I gave $X_i\sim N(\mu=8, \sigma^2=1)$ for $i=1,...91$ with observed $\bar{x}=7.319$ and I calculate $f(\bar{x}=7.319|\mu_0=8)$ and I stuck in one step of calculation, actually the very first: $(\frac{1}{\sigma\sqrt{2\pi}})^n \exp(-\frac{\sum…
Lil'Lobster
  • 179
0
votes
1 answer

Explain the following derivation

Can you explain the derivation in the given image? Which steps lead to the incorrect conclusion?
Ganesh Satpute
  • 101
0
votes
2 answers

Can two the sum of two primitive perfect squares be equal? $a^2+b^2 = c^2 + d^2$?

Given a primitive perfect square, $n^2=a^2+b^2$ where $gcd(a, b) = 1$ and $m^2=c^2+d^2$ where $gcd(c,d)=1$ Can $n=m$? a, b, c, d, n, and m are positive integers. And I forgot to mention: EDIT 1: Two of (n, a, b) are divisible by 3. One of (n, a, b)…
Stoddard
  • 25
0
votes
1 answer

How to find $\cot (x)$ of this square?

So according to question, what values of $\cot (x)$? So I've tried and got $\frac{-1}{4}$ Thanks for helping!
Physicer
  • 109
0
votes
1 answer

What will be the cube root of the number obtained from the given information?

$6bcde$ is a five-digit number. If $6-d=x, c=y$ and $xy$ is a two digit square number in which each digit is a square number. If $b = p$, $e = q$ and $pq$ is a two-digit perfect square number in which each digit cube, the cube root of $6bcde$…
Prithvish Baidya
  • 153
0
votes
2 answers

Sums of squares minus square of sums

I have the following equation in a statistics textbook and cannot see how the right side comes into being. $$\frac{1}{n} \sum_{i=1}^n x^2_i - \left(\frac{1}{n} \sum_{i=1}^n x_i\right)^2 = \frac{1}{n} \sum_{i=1}^n (x_i-\bar{x_n})^2 $$
user327281
  • 1
0
votes
1 answer

Sum implies null product. True?

Let $x, y, z \in \mathbb{C}$. Assuming that $x+y+z=x^2+y^2+z^2=0$, is it true that $x^2y^2+y^2z^2+z^2x^2=0$?
johnnaser
  • 11
  • 1
0
votes
4 answers

What is 100,000 as a sum of some number of distinct squares?

I cannot find the solution to this problem. It is part of a larger homework question but I can't go on until I solve this question.
user298365
  • 17
-1
votes
2 answers

Clarification of sums of squares formula

I’m trying to find all the ordered sums of squares: $n=x^2+y^2$, $0\leq x\leq y$ for particular $n$. I’m confused about the sum of squares formula presented on Wolfram Alpha “ To find in how many ways a positive integer n>1 can be expressed as a sum…
no lemon no melon
  • 2,129
-1
votes
1 answer

All triples of higher powers, if that were true, would be reducible to Pythagorean triples?

Here is a basic geometric argument. Consider the sum 3^2 + 4^2 = 5^2. We can represent this as three "squares" of ones, such as: 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 + 1 1 1 1 = 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 1 …
aplewe
  • 1
-1
votes
1 answer

How to open square brackets of the sum?

For example Σ(y[i]-mean(y[i]))^2 = ? Please describe the way how it opens.
ZsideZ
  • 1
1
2