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How to prove {a^(n^2) | n>0} is not context-free?

So I have a language: $$L = \{a^{n^2} \mid n > 0\}$$ I need to prove that this language isn't context-free using the pumping lemma. I have a vague thought process as to how to do the proof but I'...
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Determine whether two languages are context free

(1) $L_1 = \{a^ib^{i+j}c^j|i,j\geq 0\}$ (2) $L_2 = \{xy | x,y \in \{0,1\}^*, x \neq y, |x| = |y| \}$ I doubt that $L_1$ is CFL. I've been trying to go with the string $s$ = $a^pb^{2p}c^p$. Thus, we ...
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Proof that a language involving $gcd$ is not context-free

How would you prove that the following language is not context-free? $$L= \{a^n b^m |\, gcd(n,m)=1 \}$$ I suspect the solution uses the pumping lemma, but I'm not sure how to apply it.
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Using the pumping lemma to prove that a language is context-free [duplicate]

I am new to automata theory. Could you give me a little hand with the correct use of the pumping lemma? I understand now how to proof a language is not context-free, but how do I use the pumping ...
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Is $a^n b^n c^n$ context-free? [duplicate]

I am new to grammars and I want to learn context free grammars which are the base of programming languages. After solving some problems, I encountered the language $$\{a^nb^nc^n\mid n\geq 1\}\,.$$ ...
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Is this language is Context-free language or not?

Is anybody can help me please to determine is this language is Context-free language or not? L={wvw | w,v∈{a,b,c}+} for example: part of the language: acbac, abcab, bbcbb not part of the language:...
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Is regular expression syntax regular?

Regular expressions are equivalent to DFA's and describe regular languages, but is the language used to construct regular expressions regular? My guess is that the original syntax (concat, | and *) ...
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Applying the context-free pumping lemma to a language with crossed nestings

For proving language $\{a^nb^mc^nd^m \mid n,m > 0\}$ is not context free. Do I have to use $z = a^pb^pc^pd^p$ as pumping lemma string where $p$ is pumping length? Or do I have to use a string that ...
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How to prove that a language is not context-free using pumping lemma

I'm trying to prove that that language isn't a context free: $L = \{ w11w \mid w\in \Sigma^* = \{0,1\}\}$ I succeed to prove that $L = ww$ isn't context free, but not the language above. What ...
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Is the language $\{a^n b^n c^i | i \leq n\}$ context free?

I'm trying to apply the CFL pumping lemma. And, I've already tried words $a^pb^p$ and $a^pb^pc^p$. Not sure where to go from here.
How can we prove that: $$L = \{ w_1\#w_2 \mid w_1 \in w_2;\; |w_2| > |w_1|;\; w_1 , w_2 \in \{0, 1\}^*\}$$ is not context-free? The language defines $w_1$ as a sub-string of $w_2$, and they ...