# Linked Questions

10answers
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### Is there possibly a largest prime number?

Prime numbers are numbers with no factors other than one and itself. Factors of a number are always lower or equal to than a given number; so, the larger the number is, the larger the pool of "...
10answers
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2answers
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### Prove that the language $\{ww \mid w \in \{a,b\}^*\}$ is not FA (Finite Automata) recognisable.

Hint: Assume that $|xy| \le k$ in the pumping lemma. I have no idea where to begin for this. Any help would be much appreciated.
1answer
359 views

I am trying to prove that the number of integer solutions of $x^2-Ny^2=1$ is infinite whenever N is a squarefree integer. For this I define norm of $a+b\sqrt N=a^2-Nb^2$. Now I prove that $a+b \sqrt ... 1answer 457 views ### Pigeonhole principle to prove division Here's a little question that we were shown in class: Let$S = \{1,2,\ldots,200\}$and let$A \subseteq S$such that$|A| = 101$. Prove that there are two elements of$A$such that one is a ... 1answer 137 views ### prove existence of integers$a,q$which satisfy the following inequality Let$x \in \mathbb{R}$and integer$Q \geq 1$. Prove: there exist integers$a$and$1 \leq q \leq Q$such that$|x - \frac aq | < \frac 1{qQ} \$ any help would be appreciated!

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