List questions from sums-of-squares

Published on 14 Apr 2026 - 18:34

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When is the sum of two squares the sum of two cubes

Published on 10 Apr 2026 - 19:03

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Represent an integer as a sum of n non-consecutive squares

Published on 10 Apr 2026 - 20:19

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Maximum length of a representation of a number as an alternating sum of squares

Published on 11 Apr 2026 - 11:20

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Largest $k$ such that $(p-k) = \lceil \sqrt{(p-2k) p} \rceil$

Published on 14 Apr 2026 - 16:28

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Prove the inequality $\sum_{i,j = 1}^n {{A_{i,j}}({x_i}^2 - {x_i}{x_j})} \ge 0 $

Published on 16 Apr 2026 - 4:48

62

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Polynomial Density Theorem

Published on 11 Apr 2026 - 15:07

139

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Represent a prime number $p$ congruent to $1$ $\pmod{3}$ by a sum of a square and $3$ times a square

Published on 14 Apr 2026 - 20:45

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In how many ways can a number be expressed as a sum of squares of two natural numbers?

Published on 10 Apr 2026 - 8:05

468

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Decomposition into three squares

Published on 11 Apr 2026 - 14:20

1.6k

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Number of integer lattice points within a circle

Published on 13 Apr 2026 - 2:59

1k

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Sum of squares of two integers divisible by five

Published on 14 Apr 2026 - 0:16

488

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Numbers represented as two different sums of squares

Published on 10 Apr 2026 - 16:00

335

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For $x+y+z=3$ prove that $4\geqq x^2y+y^2z+z^2x$

Published on 10 May 2026 - 18:27

900

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sum of square root of primes 2

Published on 14 Apr 2026 - 19:36

List Question

$ 7\mid x \text{ and } 7\mid y \Longleftrightarrow 7\mid x^2+y^2 $

When is the sum of two squares the sum of two cubes

Represent an integer as a sum of n non-consecutive squares

Maximum length of a representation of a number as an alternating sum of squares

Largest $k$ such that $(p-k) = \lceil \sqrt{(p-2k) p} \rceil$

Prove the inequality $\sum_{i,j = 1}^n {{A_{i,j}}({x_i}^2 - {x_i}{x_j})} \ge 0 $

Polynomial Density Theorem

Represent a prime number $p$ congruent to $1$ $\pmod{3}$ by a sum of a square and $3$ times a square

In how many ways can a number be expressed as a sum of squares of two natural numbers?

Decomposition into three squares

Number of integer lattice points within a circle

Sum of squares of two integers divisible by five

Numbers represented as two different sums of squares

For $x+y+z=3$ prove that $4\geqq x^2y+y^2z+z^2x$

sum of square root of primes 2

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