# Questions tagged [sums-of-squares]

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

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### 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 ...
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### 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 ...
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### 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 ...
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### why sum of squares equals to assign the variable evenly in linear programming

I have a quesiton about linear programming. My objective is trying to make the utilization evenly. Example $U_{1}, U_{2},...,U_{k}$ $\sum_{i=1..k} U_{i} = C$ $C$ is some constant. $U_{i}$ is ...
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### Can Gauss-Newton algorithm give better optimization performances than Newton algorithm?

I am currently facing the problem of a robotic manipulator calibration: the goal is to find the best correction that must be applied to a set of kinematic parameters describing the robot model, in ...
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### How to interpret this visual proof for Archimedes' derivation of Sum of Squares?

I'm interested in knowing how was the first closed form solution of the sum of squares derived (for historical context/curiosity). I stumbled across an MAA Page that provides a visual proof, without ...
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### The sum of the squares of $5$ consecutive primes is again prime. True for infinite many quintuples?

Let $(p,q,r,s,t)$ be a quintuple of consecutive primes. Are there infinite many such tuples such that $$p^2+q^2+r^2+s^2+t^2$$ is prime again ? Motivation : $p^2$ is never prime $p^2+q^2$ is ...