# Questions tagged [sums-of-squares]

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

107 questions with no upvoted or accepted answers
Filter by
Sorted by
Tagged with
188 views

### Standalone proof of a conditional part of Lagrange’s Four-Square Theorem?

Lagrange’s Four-Square Theorem — a special case of the Fermat-Cauchy Polygonal Number Theorem (FCPNT) — states that every natural number can be written as the sum of the squares of at most four ...
232 views

### Looking for all sequences such that $a_i^2+a_j^2=a_k^2+a_l^2$ whenever $i^2+j^2=k^2+l^2$

I'm working in a difficult functional equation, and I have reduced the problem to the following question ($\mathbb{N}$ denotes the set of non negative integers $0,1,2,3,4\cdots$) Question: Can we ...
348 views

### Yet an other conjecture about odd numbers $n=a+b$ such that $a^2+b^2$ is prime

This question is related to A conjecture about an unlimited path and Any odd number is of form $a+b$ where $a^2+b^2$ is prime but I present it on its own if anyone would like to help finding ...
111 views

94 views

### Find the number of positive integer solutions to the equation $a^2+b^2 = p_1p_2p_3$

Find the number of positive integer solutions to the equation $$a^2+b^2 = p_1p_2p_3$$ where the $p_i$ are distinct primes each congruent to $1$ mod $4$. My take: We can show each $p_i$ can be ...
80 views

120 views

### Hypergeometric function 3F2 with unit argument

Recently I obtained the following expression $${}_3F_2(-n,a - b ,1-b-n; b + 1, 1-a-n; 1),$$ with $b>a>0$ and $n\in\mathbb{N}$. My question is: If someone knows a closed form solution to the ...
97 views

### Numbers that are the sum of 2 distinct nonzero squares in exactly 1 way

Is there a formula that says if a number is the sum of 2 distinct nonzero squares ? This is the sequence I'm trying to emulate: 5, 10, 13, 17, etc.. http://oeis.org/A004431 (Invalid it contains 85, ...
68 views

58 views

### Finding the pdf of sum of squared weighted gaussian variables

I have 3 sets of weighted gaussians that are part of 3 different Gaussian Mixture Models, phi1,phi2 and phi3. phi1 has n1 gaussian components with weights wj, mean mu_j and variance eta_j_squared, j ...
I am given a number and I have to find number of ways to present that number as sum of no more than 4 squares.For example $25$ can be presented as $1^2+2^2+2^2+4^2$, $3^2+4^2$ and $5^2$.