Intereting Posts

Orientation and simplicial homology
Given a fixed prime number $p$ and fixed positive integers $a$ and $k$; Find all positive integers $n$ such that $p^k \mid a^n-1$
Prove by induction that for all $n \geq 3$: $n^{n+1} > (n+1)^n$
Proof of $m \times a + n \times a = (m + n) \times a$ in rings
Intermediate Value Theorem and Continuity of derivative.
How do you plot the graph of $y = \sin(x)+\cos(x)$ by converting it to another form?
Proving $2,3,1+\sqrt{-5}$ and $1-\sqrt{-5}$ are irreducible in $\mathbb{Z}$
Points of continuity of a function being dense
Topology of the power set
How does one actually show from associativity that one can drop parentheses?
Matrix Inverses and Eigenvalues
The product of two positive definite matrices has real and positive eigenvalues?
Low-dimensional Irreducible Representations of $S_n$
Reformulation of Goldbach's Conjecture as optimization problem correct?
A fair coin is tossed $n$ times by two people. What is the probability that they get same number of heads?

Find a prime number $p$ and an integer $b<p$ such that $p$ divides $b^{p−1}−1$.

First I think of long divisions but it didn’t work out. Now I’m stuck..

- Infinite Prime Numbers: With Fermat Numbers
- Why can't prime numbers satisfy the Pythagoras Theorem? That is, why can't a set of 3 prime numbers be a Pythagorean triplet?
- $(m, m+2)$ is twin prime, iff $4((m-1)! + 1) \equiv -m \pmod {m(m+2)}$
- Prime numbers stretch to infinity, but what about the distance between them?
- Are the primes found as a subset in this sequence $a_n$?
- Proving there are infinitely many primes of the form $a2^k+1.$

- Are there any Combinatoric proofs of Bertrand's postulate?
- Least rational prime which is composite in $\mathbb{Z}$?
- Does $\sum\limits_{n=1}^{\infty}\frac{1}{P_n\ln(P_n)}$ converge to the golden ratio?
- Distribution of primes?
- $\text{lcm}(1,2,3,\ldots,n)\geq 2^n$ for $n\geq 7$
- Why is it that the product of first N prime numbers + 1 another prime?
- Asymptotic expression for sum of first n prime numbers?
- Sequence of numbers with prime factorization $pq^2$
- Primality of number 1
- Are there any elegant methods to classify of the Gaussian primes?

Hint; You can Make $p=3$ and $b=2$.

- Dimension of the image of the morphism associated to a Divisor
- Arrow's Impossibility Theorem and Ultrafilters. References
- What is the exact difficulty in defining a point in Euclidean geometry?
- Calculate on which side of a straight line is a given point located?
- Prove that the interval $(0, 1)$ and the Cartesian product $(0, 1) \times (0, 1)$ have the same cardinality
- Congruent Polynomials
- Why the determinant of a matrix with the sum of each row's elements equal 0 is 0?
- Further Reading on Stochastic Calculus/Analysis
- Geometrical interpretation of Ricci curvature
- Calculate $\tan9^{\circ}-\tan27^{\circ}-\tan63^{\circ}+\tan81^{\circ}$
- To what extent are the Jordan-Chevalley and Levi Decompositions compatible.
- Show that are logically equivalent
- Does algorithmic unsolvability imply unsolvability in general?
- $(p \implies q) \wedge (q \implies r) \implies (p \implies r)$
- Prove that $\cos (A + B)\cos (A – B) = {\cos ^2}A – {\sin ^2}B$