diff --git a/hw/hw8/hw8.fdb_latexmk b/hw/hw8/hw8.fdb_latexmk
index ebab914..18cbf18 100644
--- a/hw/hw8/hw8.fdb_latexmk
+++ b/hw/hw8/hw8.fdb_latexmk
@@ -1,7 +1,7 @@
 # Fdb version 4
-["pdflatex"] 1700084366 "/home/rushil/school/math/hw/hw8/hw8.tex" "hw8.pdf" "hw8" 1700084366 0
+["pdflatex"] 1700084743 "/home/rushil/school/math/hw/hw8/hw8.tex" "hw8.pdf" "hw8" 1700084743 0
   "/etc/texmf/web2c/texmf.cnf" 1693368362 475 c0e671620eb5563b2130f56340a5fde8 ""
-  "/home/rushil/school/math/hw/hw8/hw8.tex" 1700084365 7904 033950536c11fc42779f3aa61d68f2e8 ""
+  "/home/rushil/school/math/hw/hw8/hw8.tex" 1700084743 7876 a6c479a981a89d878f1c91417a8dea27 ""
   "/usr/share/texlive/texmf-dist/fonts/map/fontname/texfonts.map" 1577235249 3524 cb3e574dea2d1052e39280babc910dc8 ""
   "/usr/share/texlive/texmf-dist/fonts/tfm/public/amsfonts/cmextra/cmex7.tfm" 1246382020 1004 54797486969f23fa377b128694d548df ""
   "/usr/share/texlive/texmf-dist/fonts/tfm/public/amsfonts/cmextra/cmex8.tfm" 1246382020 988 bdf658c3bfc2d96d3c8b02cfc1c94c20 ""
@@ -149,8 +149,8 @@
   "/usr/share/texmf/web2c/texmf.cnf" 1681034085 39561 34c98e380bf7c7201ee6a7909aff625a ""
   "/var/lib/texmf/fonts/map/pdftex/updmap/pdftex.map" 1693368379 4623455 fa0568a71dd9a288d6c226ee477506c6 ""
   "/var/lib/texmf/web2c/pdftex/pdflatex.fmt" 1693368408 7880218 5644a8bb2704ddc1060e0c139ce5389a ""
-  "hw8.aux" 1700084366 194 88c1331b9e58d48c539d01f9d282ed72 "pdflatex"
-  "hw8.tex" 1700084365 7904 033950536c11fc42779f3aa61d68f2e8 ""
+  "hw8.aux" 1700084743 194 88c1331b9e58d48c539d01f9d282ed72 "pdflatex"
+  "hw8.tex" 1700084743 7876 a6c479a981a89d878f1c91417a8dea27 ""
   (generated)
   "hw8.aux"
   "hw8.log"
diff --git a/hw/hw8/hw8.log b/hw/hw8/hw8.log
index b8d3a98..14711cb 100644
--- a/hw/hw8/hw8.log
+++ b/hw/hw8/hw8.log
@@ -1,4 +1,4 @@
-This is pdfTeX, Version 3.141592653-2.6-1.40.24 (TeX Live 2022/Debian) (preloaded format=pdflatex 2023.8.30)  15 NOV 2023 16:39
+This is pdfTeX, Version 3.141592653-2.6-1.40.24 (TeX Live 2022/Debian) (preloaded format=pdflatex 2023.8.30)  15 NOV 2023 16:45
 entering extended mode
  restricted \write18 enabled.
  file:line:error style messages enabled.
@@ -489,7 +489,7 @@ Here is how much of TeX's memory you used:
  1141 hyphenation exceptions out of 8191
  102i,11n,104p,488b,290s stack positions out of 10000i,1000n,20000p,200000b,200000s
 </usr/share/texlive/texmf-dist/fonts/type1/public/amsfonts/cm/cmbx10.pfb></usr/share/texlive/texmf-dist/fonts/type1/public/amsfonts/cm/cmbx12.pfb></usr/share/texlive/texmf-dist/fonts/type1/public/amsfonts/cm/cmbx9.pfb></usr/share/texlive/texmf-dist/fonts/type1/public/amsfonts/cm/cmmi10.pfb></usr/share/texlive/texmf-dist/fonts/type1/public/amsfonts/cm/cmr10.pfb></usr/share/texlive/texmf-dist/fonts/type1/public/amsfonts/cm/cmr7.pfb></usr/share/texlive/texmf-dist/fonts/type1/public/amsfonts/cm/cmr9.pfb></usr/share/texlive/texmf-dist/fonts/type1/public/amsfonts/cm/cmsl10.pfb></usr/share/texlive/texmf-dist/fonts/type1/public/amsfonts/cm/cmsy10.pfb></usr/share/texlive/texmf-dist/fonts/type1/public/amsfonts/cm/cmti10.pfb></usr/share/texlive/texmf-dist/fonts/type1/public/amsfonts/cm/cmti12.pfb></usr/share/texlive/texmf-dist/fonts/type1/public/amsfonts/symbols/msbm10.pfb>
-Output written on hw8.pdf (8 pages, 140306 bytes).
+Output written on hw8.pdf (8 pages, 140299 bytes).
 PDF statistics:
  94 PDF objects out of 1000 (max. 8388607)
  59 compressed objects within 1 object stream
diff --git a/hw/hw8/hw8.pdf b/hw/hw8/hw8.pdf
index a8d1650..bf0f20b 100644
Binary files a/hw/hw8/hw8.pdf and b/hw/hw8/hw8.pdf differ
diff --git a/hw/hw8/hw8.synctex.gz b/hw/hw8/hw8.synctex.gz
index 0c6bb62..2256084 100644
Binary files a/hw/hw8/hw8.synctex.gz and b/hw/hw8/hw8.synctex.gz differ
diff --git a/hw/hw8/hw8.tex b/hw/hw8/hw8.tex
index fea23a3..2c81adb 100644
--- a/hw/hw8/hw8.tex
+++ b/hw/hw8/hw8.tex
@@ -147,8 +147,6 @@ Prove that if \(a\) and \(b\) are nonzero integers, \(a | b\), and \(a + b\) is
 \pagebreak
 \prob{26}
 Evaluate these quantites:
-\begin{align*}
-\end{align*}
 \begin{enumerate}[a)]
     \item \(-17 \textbf{ mod } 2\) = \hspace{12pt} 1
     \item \(144 \textbf{ mod } 7\) = \hspace{14pt} 4