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Prove that if a prime $p$ divides $a^2 + b^2$ then it must divide both a and b.

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#number-theory #prime-numbers #pythagorean-triples
109
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$k^*/k^{*2}$ is a vector space?

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#number-theory
396
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Let p be a prime number

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#number-theory #factorial #congruences
105
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Integer Solutions to an Ellipse from Parameterization?

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#number-theory #conic-sections
216
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Egyptian fraction decomposition of $1$ and the sequence A007018.

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#number-theory #determinant #diophantine-equations
71
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Fermat's theorem

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#number-theory
261
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Finding Solutions to a Simultaneous Linear Equation

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#number-theory #modular-arithmetic #systems-of-equations
72
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Goldbach's Conjecture and 1-1 correspondence

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#number-theory #goldbachs-conjecture
86
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How to interpret $\left(\begin{smallmatrix}p_n & p_{n-1}\\ q_n & q_{n-1}\end{smallmatrix}\right)$?

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#matrices #number-theory #continued-fractions
183
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The notation $f < o(g)$ and $f > o(g)$ from the Landau family of asymptotic notations

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#real-analysis #number-theory #analysis #asymptotics #computer-science
55
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How to prove that $\frac 1{q_{n+2}}\leq \left|p_{n}-bq_n\right|$?

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#number-theory #elementary-number-theory #inequality #fractions #continued-fractions
56
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How to prove that $x=\frac{p_n+p_{n-1}x_{n+1}}{p_n+p_{n-1}x_{n+1}}$

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#number-theory #elementary-number-theory #fractions #ergodic-theory #continued-fractions
187
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Show that $n+1$ is prime if (Denominator(Bernoulli Number($n$)))/($n+1$) is an integer

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#calculus #sequences-and-series #number-theory #prime-numbers #bernoulli-numbers
37
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PIE in twisted manner

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#number-theory
59
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Simplest Basis to find the mobius function?

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#number-theory #functional-equations #coordinate-systems #mobius-function

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