Intereting Posts

Iterated Integrals and Riemann-Liouville (Fractional) Derivatives
Finding all real roots of the equation $(x+1) \sqrt{x+2} + (x+6)\sqrt{x+7} = x^2+7x+12$
When does $\sqrt{wz}=\sqrt{w}\sqrt{z}$?
Prove that the function $f(z)=(Arg z)^2$ is continuous in the punctured plane $\Bbb C \setminus\{0\}$
Problem about limit of Lebesgue integral over a measurable set
Factoring $ac$ to factor $ax^2+bx+c$
The staircase paradox, or why $\pi\ne4$
The cardinality of Indra's net?
Why is the Laplacian important in Riemannian geometry?
Accumulation points of uncountable sets
The right “weigh” to do integrals
Convergence of $\sum_n \frac{|\sin(n^2)|}{n}$
Prove the existence of $c$ such that $f'(c) = 2c(f(c) – f(0))$
Combinatorics – pigeonhole principle question
Why metrizable group requires continuity of inverse?

Let $k \geq 2$ be a positive integer and let $n=2^k+1$. How can I prove that $n$ is a prime number if and only if

$$3^{\frac{n-1}{2}} \equiv -1 \pmod n.$$

*Fixed.*

- Proof that Fibonacci Sequence modulo m is periodic?
- When does $A(x^2+y^2+z^2)=B(xy + yz + xz)$ have nontrivial integer solutions?
- Prove that if $\gcd( a, b ) = 1$ then $\gcd( ac, b ) = \gcd( c, b ) $
- If $\gcd(a,b)=1$ and $\gcd(a,c)=1$, then $\gcd(a,bc)=1$
- Is knowing the Sum and Product of k different natural numbers enough to find them?
- $g^k$ is a primitive element modulo $m$ iff $\gcd (k,\varphi(m))=1$

- Higher dimensional analogues of the argument principle?
- prove that $x^2 + y^2 = z^4$ has infinitely many solutions with $(x,y,z)=1$
- Prove that $2^{10}+5^{12}$ is composite
- Are there useful criterions whether a positive integer is the difference ot two positive cubes?
- The Diophantine equation $x^2 + 2 = y^3$
- Power residue theorem without p-adic method
- Smallest number with specific number of divisors
- Why $Z_p$ is closed.
- Alternating sum of multiple zetas equals always 1?
- Sums of Consecutive Cubes (Trouble Interpreting Question)

Here are two options for finding a proper proof for this theorem (called Pepin’s test).

1) http://en.wikipedia.org/wiki/Pepin's_test.

2) “Solved and Unsolved Problems in Number Theory” by Daniel Shanks.

This book includes the proof for that theorem.

This is the simplest case of Pratt certificates for primality – have a look at http://mathworld.wolfram.com/PrattCertificate.html for a better explanation. (In the notation of the article, your question corresponds to the case where the only $p_i$ is $2$.)

- nondimensionalization of predator-prey model
- Finding the area of a implicit relation
- Colimits glue. What do limits do?
- Global class field theory without p-adic method
- Can anybody explain about real linear space and complex linear space?
- How do I exactly project a vector onto a subspace?
- Proving the last part of Nested interval property implying Axiom of completeness
- Why is a matrix $A\in \operatorname{SL}(2,\mathbb{R})$ with $|\operatorname{tr}(A)|<2$ conjugate to a matrix of the following form?
- Integration of $\displaystyle \int\frac{1}{1+x^8}\,dx$
- Showing $\log(2)$ and $\log(5)$
- Are all subrings of the rationals Euclidean domains?
- the number of loops on lattice?
- How to prove that sections of family of curves do not exist (exercise 4.7 in Harris' Algebraic Geometry)?
- (Non-)Conservative Vector Fields
- Universal cover of $\mathbb R^2\setminus\{0\}$