# 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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### Relationship between the squares of first n natural numbers and first n natural odd numbers.

Here's a question from high school mathematics. If $1^2 + 2^2 + 3^2 + 4^2 + 5^2 + \dots + 100^2 = x$, then ($1^2 + 3^2 + 5^2 + \dots + 99^2$) is equal to ? Options were: (a) $\frac{x}{2}-2525$ (b) ...
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### What numbers can be written uniquely as a sum of two squares?

What numbers can be written uniquely as a sum of two squares? I was looking at sequence A125022, which shows the numbers that can be uniquely written as a sum of two squares. Here are a few things ...
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### Integers that are sums of two squares [duplicate]

It is easy to decide if a given integer $n$ is the sum of two squares, and in fact there is a simple formula (based on the prime factorization) to compute the number of ways that $n$ can be written as ...
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### Consequence following from the hypothesis $: 7$ divides $a^2 + b^2$ with $a, b \in \mathbb Z$ [duplicate]

Not HM, simply self teaching. Source : Alain Troesch (Louis-le-Grand High School, Paris) , Exercices $2022-2023$, Polycopié des exercices , page $99$, Ex. $21.10$ http://alain.troesch.free.fr/ ...
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### Sequence of squares which can't be written as the sum of a smaller non-zero square and twice a triangular number

Are there infinitely many squares which cannot be written as the sum of a smaller non-zero square and twice a triangular number? In other words, is the list given at https://oeis.org/A230312 infinite? ...
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### Writing 2024 as the sum of 3 and 4 squares

I'm currently taking a course in number theory and we've just seen that any number can be written as the sum of the 4 squares, and that numbers can be written as the sum of 3 if they aren't of a ...
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### How do I calculate the prediction interval for a data set in python?

I have a data set taken from real measurements that I have modeled with a simple univariate linear regression in python using scipy.stats.linregress, so the model ...
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### Show that the sum is between (1,2) [closed]

Show that the sum $$1+\frac{1}{2^2}+\frac{1}{3^2}+\dots+ \frac{1}{2022^2}$$ is between $(1,2)$, I mean is bigger than $1$ and less than $2$. What I tried: honestly I never knew or understood how to ...
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