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Results tagged with nt.number-theory
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user 95032
Prime numbers, diophantine equations, diophantine approximations, analytic or algebraic number theory, arithmetic geometry, Galois theory, transcendental number theory, continued fractions
6
votes
1
answer
446
views
Are there an infinite number of integers $n$ such that $n, n+1$, and $n+2$ have the same num...
Is the set $S:=\{n\in\mathbb{N} \mid \text{$n$, $n+1$ and $n+2$ have the same number of divisors}\}$ infinite?
Example: $33\in S$.
11
votes
3
answers
2k
views
Is there any formula to find number of Pythagorean triplets between two integers 2 and j, j>2?
Given $j \geq 5$, is there a formula for the number of Pythagorean triplets $(a, b, c)$ satisfying the constraint that $a, b, c \leq j$?
There exists at least one Pythagorean triplet for $j\geq5$; th …