Questions on congruences, linear diophantine equations, greatest common divisor, divisibility, etc.

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14
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0answers
668 views
+100

Are there unique solutions for $n=\sum_{j=1}^{g(k)} a_j^k$?

Edward Waring, asks whether for every natural number $n$ there exists an associated positive integer s such that every natural number is the sum of at most $s$ $k$th powers of natural numbers ...
3
votes
1answer
159 views
+50

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

How to prove that this conjecture is true ? Definition : $\text{Let}~ P_m(x)=2^{-m}\cdot \left(\left(x-\sqrt{x^2-4}\right)^{m}+\left(x+\sqrt{x^2-4}\right)^{m}\right)~ , \text{where}~ m ~\text{and}~ x ...
8
votes
1answer
125 views
+50

Determine all one to one functions $f:\mathbb{N}^* \rightarrow \mathbb{N}^*$ having the following property:

Determine all one to one functions $f:\mathbb{N}^* \rightarrow \mathbb{N}^*$ (where $\mathbb{N}^*$ means all positive integers) having the following property: For all $S$, where $S$ is a finite set ...