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

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### Squares in Lucas sequences

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

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

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### Good upper bound for a certain sum

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

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### 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 $\mu \in \Delta_k$

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

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

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

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### How to define $``\ll"$ in higher dimension?

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### Products and sum of cubes in Fibonacci

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### Reference for calculating definite integral involving sines

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

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