# Questions tagged [elementary-proofs]

For questions related to 'elementary' proofs in a technical sense, which has nothing to do with the difficulty of the argument or result. A typical example would be 'elementary' proofs of the Prime Number Theorem, which avoid complex analysis. The tag is however not limited to this particular notion of 'elementary.'

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### Primality test for specific class of $N=8kp^n-1$

**5**

**1**answer

### Conjectured primality test for specific class of $N=k \cdot 6^n+1$

**4**

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### How to prove there is infinite prime numbers of form $5n+3$ without Dirichlet theorem? [closed]

**1**

**3**answers

### Perfect squares between certain divisors of a number

**-2**

**1**answer

### Diophantine equation $10^n-a^3-b^3=c^2$

**2**

**2**answers

### “Strengthening” the mean value theorem for the sine function

**5**

**4**answers

### Combinatorial proof of Catalan's identity

**4**

**2**answers

### Largest absolute value of a polynomial of degree $n$ on $\{0,1,\ldots,n\}$

**0**

**0**answers

### Exponential sums involving completely multiplicative functions

**0**

**1**answer

### Can I get away without using Arzela-Ascoli?

**0**

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### Number of distinct terms in the dRRS for n

**0**

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### Some questions in a paper by E. H. Neville (1949) about Farey series?

**8**

**2**answers

### Area method in Lobachevskian geometry

**1**

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### The $p$-adic valuation of powers of consecutive integers

**3**

**1**answer

### Squares in Lucas sequences

**2**

**0**answers

### Average number of pieces of a random piecewise-linear function

**2**

**0**answers

### Conjectured primality test for numbers of the form $N=4 \cdot 3^n-1$

**3**

**2**answers

### Good upper bound for a certain sum

**7**

**2**answers

### A set, product of any two elements minus one is a perfect square

**2**

**0**answers

### Bounds for $\sum_{t=1}^Tn_t(s_t)^{-\alpha}\mu(s_t)$ where $n_t(s) = \sum_{1 \le t' \le t} 1_{\{s_{t'}=s\}}$ for $s \in [k]$ and $\mu \in \Delta_k$

**11**

**1**answer

### Diophantine equation $3^a+1=3^b+5^c$

**5**

**1**answer

### What was the first elementary proof that $\pi(x)=o(x)$?

**1**

**1**answer

### Formally proving that a metric is not induced by any norm in $\mathbb{R}^n$ [closed]

**6**

**2**answers

### Products and sum of cubes in Fibonacci

**3**

**0**answers

### Reference for calculating definite integral involving sines

**11**

**1**answer

### Is there an elementary proof that there are infinitely many primes that are *not* completely split in an abelian extension?

**2**

**1**answer

### Partitioning the positive integers into finitely many arithmetic progressions

**12**

**3**answers

### Does anyone recognize this inequality?

**1**

**1**answer

### Good UPPER bounds for $\log(\sum_{i=1}^n p_ie^{z_i})-\sum_{i=1}^np_iz_i$ where $(p_i)_i$ is a probability vector

**4**

**2**answers

### Is the following recursion formula for $\zeta(2n)$ known?

**10**

**2**answers

### Sum of squared nearest-neighbor distances between points in a square

**22**

**15**answers

### Geodesics on the sphere

**6**

**2**answers

### How often does the Mertens function vanish?

**7**

**4**answers

### Different derivations of the value of $\prod_{0\leq j<k<n}(\eta^k-\eta^j)$

**2**

**2**answers

### Prove that there exists a nonempty subset $ I$ of $ \{1,2,…,n\}$ such that $ \sum_{i\in I}{\frac {1}{b_i}}$ is an integer

**9**

**2**answers

### Certain matrices of interesting determinant

**21**

**2**answers

### A Putnam problem with a twist

**1**

**0**answers

### Supremum of an almost surely continuous random process

**10**

**1**answer

### A set of prime numbers

**2**

**1**answer

### On submatrices: size bound

**2**

**1**answer

### Vandermonde determinant: modulo

**3**

**1**answer

### Generating function for 3 -core partitions: Part II

**8**

**1**answer

### Generating function for $3$-core partitions

**7**

**2**answers

### A link between hooks and contents: Part II

**6**

**2**answers

### A link between hooks, contents and parts of a partition

**16**

**2**answers

### Why are the medians of a triangle concurrent? In absolute geometry

**21**

**1**answer

### A proof required for this identity [duplicate]

**1**

**1**answer

### Primality test for generalized Fermat numbers

**0**

**1**answer

### $2$-adic valuations and sum of divisor function

**9**

**1**answer