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Prove for every $m, n$, $(m^2 - n^2, 2mn, m^2 + n^2)$ can make pythagorean triple

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#elementary-number-theory #pythagorean-triples
261
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Role of binomial coefficents in nested summations in layman terms

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#sequences-and-series #elementary-number-theory #summation #binomial-coefficients #intuition
99
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Find a specific solution to a linear Diophantine equation

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#elementary-number-theory #euclidean-algorithm #linear-diophantine-equations
316
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Find the value of an integer $a$ such that $ a^2 +6a +1 $ is a perfect square.

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#number-theory #elementary-number-theory #quadratics
2.2k
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Divisibility 1,2,3,4,5,6,7,8,9,&10

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#elementary-number-theory #divisibility #factoring #decimal-expansion #divisible-groups
245
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Finding primitive roots modulo $x$

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#number-theory #elementary-number-theory #primitive-roots
1.4k
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Number of steps of Euclidean algorithm. why $r_i{_+}_2 < \frac{1}{2}r_i$?

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#number-theory #elementary-number-theory #euclidean-algorithm
61
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Independence of random products mod $p$

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#probability #number-theory #elementary-number-theory #statistics
503
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Descent in proof of Euclid's Lemma: prime $\,p\mid bc\Rightarrow p\mid b\,$ or $\,p\mid c$

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#elementary-number-theory #proof-explanation
111
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sum of multiplicative inverses for $p=3k+1$

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#number-theory #elementary-number-theory
207
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last 4 digits of $7^{65}$

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#elementary-number-theory #modular-arithmetic
350
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How many $4$ digit integers have the product of their digits equal to $5!$?

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#combinatorics #elementary-number-theory
179
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Amount of P-smooth numbers inside a given interval

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#elementary-number-theory #prime-numbers
63
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Since $\Bbb{Z}/(p)$ is a ring and $(\Bbb{Z}/p)^{\times} \simeq \Bbb{Z}/(p-1)$ which is also a ring, how do they relate?

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#abstract-algebra #elementary-number-theory #prime-numbers #modular-arithmetic #integers
862
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Finding the last 4 digits of a huge power

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#number-theory #elementary-number-theory #modular-arithmetic #problem-solving

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