math-modesymbols
The symbol for modularly congruent is ≡, which can be produced with \equiv.
For instance,
18 ≡ 0 (mod 9)
What is the symbol for not modularly congruent, and how do I represent it in TeX?
I have perused some references including http://web.ift.uib.no/Teori/KURS/WRK/TeX/symALL.html and have not found it.
I found it in the Journal of Combinatorial Optimization (2007) 13:217-221, February 14, 2007:
A 2-approximation for the preceding-and-crossing structured 2-interval pattern problem. There the expression \{<,\between\} has been used, as can be seen in the abstract.
Regarding intervals, \between 
may stand for a crossing/overlapping relation like < for a precedence order and kind of a subset symbol for inclusion/nesting. See also Extracting constrained 2-interval subsets in 2-interval sets.
In such difficult cases, the LaTeX search engine of Springer is a useful tool (now discontinued).
The character bounding box of \Box is wrong, the height is too low, when latexsym is used as package to get the symbol:
\documentclass{article}
\usepackage{amsmath,latexsym}
\begin{document}
\setlength{\fboxsep}{0pt}
\setlength{\fboxrule}{.1pt}
\[ \fbox{$\Box$} \fbox{$\hat\Box$} \fbox{$\tilde\Box$} \]
\begin{align*}
\Box &= \sum_a \partial^a\partial_a \,, &
\hat\Box &= \sum_a \mathcal{D}^a\mathcal{D}_a
\end{align*}
\end{document}
Using amssymb instead fixes the issue:
\documentclass{article}
\usepackage{amsmath,amssymb}
\begin{document}
\setlength{\fboxsep}{0pt}
\setlength{\fboxrule}{.1pt}
\[ \fbox{$\Box$} \fbox{$\hat\Box$} \fbox{$\tilde\Box$} \]
\begin{align*}
\Box &= \sum_a \partial^a\partial_a \,, &
\hat\Box &= \sum_a \mathcal{D}^a\mathcal{D}_a
\end{align*}
\end{document}
Best Answer
Negation of symbols in LaTeX is typically achieved prepending it with
\not. For exampleFor more elaborate, larger or lengthy symbols, you can use the
cancelpackage. In those instances\notmay not provide a sufficiently-centred negation. Thecenternotpackage also provides a centred\notfor symbols with larger horizontal dimension.The ≢ character is in Unicode as U+2262, and can be entered directly with
unicode-math. The command for it is\nequivin many packages, includingunicode-math,pxfonts,txfonts,newpxmath,newtxmath,stix,stix2,mnsymbolandfdsymbol.Other symbol-lookup techniques are described in How to look up a symbol or identify a math symbol or character?