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Results tagged with nt.number-theory
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user 18229
Prime numbers, diophantine equations, diophantine approximations, analytic or algebraic number theory, arithmetic geometry, Galois theory, transcendental number theory, continued fractions
-1
votes
1
answer
116
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Fractional equations [closed]
Let’s have the equation $a^k+\frac{k \cdot a^k}{x \cdot y^n}=m^k$ where $k≥2$ and $x≠y$ and $a, k, x, y, n, m$ positive integers greater than zero. If $x \cdot y^n = f \cdot a^g$ where $f$ and $g$ an …
0
votes
0
answers
108
views
Right angle parallelepipeds with the same greatest diagonal (the sides and greatest diagonal...
Let’s have the equation
$$(r_1\times p+p)^4-(4r_1^3+6r_1^2+4r_1+1)\times p^4=(r_1\times p)^4$$
And if $p=2$ and $r_1=n/2$ where $n$ a positive integer the above equation is written as follows:
…
8
votes
1
answer
2k
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prime numbers and Pythagorean triplets
What are the necessary conditions for two of the terms in the Pythagorean triplet $a^2 = b^2 + c^2$ to be prime numbers?