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Given an integer, how can I detect the nearest integer perfect power efficiently?
number-theory
polynomials
algebraic-number-theory
exponentiation
perfect-powers
Find all positive integers $n$ for which $1372n^4 - 3 $ is an odd perfect square.
number-theory
elementary-number-theory
diophantine-equations
square-numbers
perfect-powers
Find last three nonzero digits of $1^1 \cdot 2^2 \cdot 3^3 \cdot ... \cdot 25^{25}$
number-theory
elementary-number-theory
modular-arithmetic
chinese-remainder-theorem
perfect-powers
Find all positive integers $a, b, c$ such that $21^a+ 28^b= 35^c$ .
algebra-precalculus
diophantine-equations
exponential-sum
perfect-powers
Find all triples $(a,b,c)$ giving $3$ powers of $3$ simultaneously [closed]
elementary-number-theory
perfect-powers
How do I prove that $3^n - 3$ is never a square number?
elementary-number-theory
square-numbers
perfect-powers
Pairwise sums are perfect squares .
number-theory
elementary-number-theory
perfect-powers
If $ a + b + c \mid a^2 + b^2 + c^2$ then $ a + b + c \mid a^n + b^n + c^n$ for infinitely many $n$
number-theory
contest-math
divisibility
perfect-powers
Prove that $\sum\limits_{k=1}^n (k!)^2$ is not a perfect square when $n\ge2$
sequences-and-series
number-theory
perfect-powers
Can you find a function $\beta(x)$ where if $a+b=n^m$ then $\beta(\frac{a}{b})$ is irrational?
real-analysis
recreational-mathematics
perfect-powers
Sums of $5$th and $7$th powers of natural numbers: $\sum\limits_{i=1}^n i^5+i^7=2\left( \sum\limits_{i=1}^ni\right)^4$?
sequences-and-series
elementary-number-theory
summation
power-series
perfect-powers
Find all natural number $n$ for which $3^9+3^{12}+3^{15}+3^n$ is a perfect cube.
elementary-number-theory
modular-arithmetic
perfect-powers
Solutions to $A^N+B^N=C^N \pm 1$
number-theory
diophantine-equations
perfect-powers
$x^2+x+1$ is the cube of a prime.
number-theory
prime-numbers
perfect-powers
Perfect powers of successive naturals: Can you always reach a constant difference?
elementary-number-theory
perfect-powers
A $\frac{1}{3}$ Conjecture?
matrices
analytic-number-theory
conjectures
perfect-powers
Product of three consecutive positive integers is never a perfect power
elementary-number-theory
contest-math
perfect-powers
Integers $n$ for which the digit sum of $n$ exceeds the digit sum of $n^5$
elementary-number-theory
inequality
decimal-expansion
perfect-powers
What is the smallest integer greater than 1 such that $\frac12$ of it is a perfect square and $\frac15$ of it is a perfect fifth power?
algebra-precalculus
diophantine-equations
integers
perfect-powers
How to compute 2-adic square roots?
number-theory
p-adic-number-theory
square-numbers
perfect-powers
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