id	topic_id	thread_id	type	formula
q_253	A.31	3082747	question	"<?xml version='1.0' encoding='UTF-8'?>
<math xmlns=""http://www.w3.org/1998/Math/MathML""><apply><ci>→</ci><ci>p</ci><ci>q</ci></apply></math>"
q_254	A.31	3082747	question	"<?xml version='1.0' encoding='UTF-8'?>
<math xmlns=""http://www.w3.org/1998/Math/MathML""><ci>p</ci></math>"
q_255	A.31	3082747	question	"<?xml version='1.0' encoding='UTF-8'?>
<math xmlns=""http://www.w3.org/1998/Math/MathML""><ci>q</ci></math>"
q_256	A.31	3082747	question	"<?xml version='1.0' encoding='UTF-8'?>
<math xmlns=""http://www.w3.org/1998/Math/MathML""><apply><ci>→</ci><ci>p</ci><ci>q</ci></apply></math>"
q_257	A.31	3082747	question	"<?xml version='1.0' encoding='UTF-8'?>
<math xmlns=""http://www.w3.org/1998/Math/MathML""><ci>p</ci></math>"
q_258	A.31	3082747	question	"<?xml version='1.0' encoding='UTF-8'?>
<math xmlns=""http://www.w3.org/1998/Math/MathML""><ci>q</ci></math>"
q_259	A.31	3082747	question	"<?xml version='1.0' encoding='UTF-8'?>
<math xmlns=""http://www.w3.org/1998/Math/MathML""><ci>p</ci></math>"
q_260	A.31	3082747	question	"<?xml version='1.0' encoding='UTF-8'?>
<math xmlns=""http://www.w3.org/1998/Math/MathML""><ci>q</ci></math>"
q_261	A.31	3082747	question	"<?xml version='1.0' encoding='UTF-8'?>
<math xmlns=""http://www.w3.org/1998/Math/MathML""><apply><ci>→</ci><ci>p</ci><ci>q</ci></apply></math>"
q_730	A.78	3237032	title	"<?xml version='1.0' encoding='UTF-8'?>
<math xmlns=""http://www.w3.org/1998/Math/MathML""><apply><apply><csymbol>superscript</csymbol><apply><csymbol>subscript</csymbol><sum/><apply><eq/><ci>n</ci><cn type=""integer"">1</cn></apply></apply><infinity/></apply><apply><csymbol>subscript</csymbol><ci>a</ci><ci>n</ci></apply></apply></math>"
q_731	A.78	3237032	title	"<?xml version='1.0' encoding='UTF-8'?>
<math xmlns=""http://www.w3.org/1998/Math/MathML""><apply><apply><csymbol>superscript</csymbol><apply><csymbol>subscript</csymbol><sum/><apply><eq/><ci>n</ci><cn type=""integer"">1</cn></apply></apply><infinity/></apply><apply><csymbol>superscript</csymbol><apply><csymbol>subscript</csymbol><ci>a</ci><ci>n</ci></apply><cn type=""integer"">2</cn></apply></apply></math>"
q_732	A.78	3237032	question	"<?xml version='1.0' encoding='UTF-8'?>
<math xmlns=""http://www.w3.org/1998/Math/MathML""><list><apply><times/><ci>italic-ε</ci><ci>&amp;</ci><ci>g</ci><ci>t</ci></apply><cn type=""integer"">0</cn></list></math>"
q_733	A.78	3237032	question	"<?xml version='1.0' encoding='UTF-8'?>
<math xmlns=""http://www.w3.org/1998/Math/MathML""><apply><sum/><apply><csymbol>subscript</csymbol><ci>a</ci><ci>n</ci></apply></apply></math>"
q_734	A.78	3237032	question	"<?xml version='1.0' encoding='UTF-8'?>
<math xmlns=""http://www.w3.org/1998/Math/MathML""><apply><geq/><list><apply><times/><ci>n</ci><ci>&amp;</ci><ci>g</ci><ci>t</ci></apply><ci>m</ci></list><ci>N</ci></apply></math>"
q_735	A.78	3237032	question	"<?xml version='1.0' encoding='UTF-8'?>
<math xmlns=""http://www.w3.org/1998/Math/MathML""><apply><eq/><apply><abs/><apply><apply><csymbol>superscript</csymbol><apply><csymbol>subscript</csymbol><sum/><apply><eq/><ci>k</ci><apply><plus/><ci>m</ci><cn type=""integer"">1</cn></apply></apply></apply><ci>n</ci></apply><apply><abs/><apply><csymbol>subscript</csymbol><ci>a</ci><ci>k</ci></apply></apply></apply></apply><list><apply><apply><csymbol>superscript</csymbol><apply><csymbol>subscript</csymbol><sum/><apply><eq/><ci>k</ci><apply><plus/><ci>m</ci><cn type=""integer"">1</cn></apply></apply></apply><ci>n</ci></apply><apply><times/><apply><abs/><apply><csymbol>subscript</csymbol><ci>a</ci><ci>k</ci></apply></apply><ci>&amp;</ci><ci>l</ci><ci>t</ci></apply></apply><apply><root/><ci>italic-ε</ci></apply></list></apply></math>"
q_736	A.78	3237032	question	"<?xml version='1.0' encoding='UTF-8'?>
<math xmlns=""http://www.w3.org/1998/Math/MathML""><apply><geq/><list><apply><times/><ci>n</ci><ci>&amp;</ci><ci>g</ci><ci>t</ci></apply><ci>m</ci></list><ci>N</ci></apply></math>"
q_737	A.78	3237032	question	"<?xml version='1.0' encoding='UTF-8'?>
<math xmlns=""http://www.w3.org/1998/Math/MathML""><apply><csymbol>formulae-sequence</csymbol><apply><and/><apply><eq/><apply><abs/><apply><apply><csymbol>superscript</csymbol><apply><csymbol>subscript</csymbol><sum/><apply><eq/><ci>k</ci><apply><plus/><ci>m</ci><cn type=""integer"">1</cn></apply></apply></apply><ci>n</ci></apply><apply><csymbol>superscript</csymbol><apply><csymbol>subscript</csymbol><ci>a</ci><ci>k</ci></apply><cn type=""integer"">2</cn></apply></apply></apply><apply><apply><csymbol>superscript</csymbol><apply><csymbol>subscript</csymbol><sum/><apply><eq/><ci>k</ci><apply><plus/><ci>m</ci><cn type=""integer"">1</cn></apply></apply></apply><ci>n</ci></apply><apply><csymbol>superscript</csymbol><apply><csymbol>subscript</csymbol><ci>a</ci><ci>k</ci></apply><cn type=""integer"">2</cn></apply></apply></apply><apply><leq/><apply><apply><csymbol>superscript</csymbol><apply><csymbol>subscript</csymbol><sum/><apply><eq/><ci>k</ci><apply><plus/><ci>m</ci><cn type=""integer"">1</cn></apply></apply></apply><ci>n</ci></apply><apply><csymbol>superscript</csymbol><apply><csymbol>subscript</csymbol><ci>a</ci><ci>k</ci></apply><cn type=""integer"">2</cn></apply></apply><apply><times/><apply><csymbol>superscript</csymbol><apply><apply><csymbol>superscript</csymbol><apply><csymbol>subscript</csymbol><sum/><apply><eq/><ci>k</ci><apply><plus/><ci>m</ci><cn type=""integer"">1</cn></apply></apply></apply><ci>n</ci></apply><apply><abs/><apply><csymbol>subscript</csymbol><ci>a</ci><ci>k</ci></apply></apply></apply><cn type=""integer"">2</cn></apply><ci>&amp;</ci><ci>l</ci><ci>t</ci></apply></apply></apply><apply><eq/><apply><csymbol>superscript</csymbol><apply><root/><ci>italic-ε</ci></apply><cn type=""integer"">2</cn></apply><ci>italic-ε</ci></apply></apply></math>"
q_738	A.78	3237032	question	"<?xml version='1.0' encoding='UTF-8'?>
<math xmlns=""http://www.w3.org/1998/Math/MathML""><apply><sum/><apply><csymbol>superscript</csymbol><apply><csymbol>subscript</csymbol><ci>a</ci><ci>n</ci></apply><cn type=""integer"">2</cn></apply></apply></math>"
q_1027	A.101	3163489	question	"<?xml version='1.0' encoding='UTF-8'?>
<math xmlns=""http://www.w3.org/1998/Math/MathML""><apply><leq/><apply><csymbol>superscript</csymbol><ci>n</ci><cn type=""integer"">2</cn></apply><apply><csymbol>superscript</csymbol><cn type=""integer"">2</cn><ci>n</ci></apply></apply></math>"
q_1028	A.101	3163489	question	"<?xml version='1.0' encoding='UTF-8'?>
<math xmlns=""http://www.w3.org/1998/Math/MathML""><apply><in/><apply><csymbol>for-all</csymbol><ci>n</ci></apply><list><ci>N</ci><apply><times/><ci>n</ci><ci>&amp;</ci><ci>g</ci><ci>t</ci></apply><cn type=""integer"">3</cn></list></apply></math>"
q_1029	A.101	3163489	question	"<?xml version='1.0' encoding='UTF-8'?>
<math xmlns=""http://www.w3.org/1998/Math/MathML""><apply><eq/><ci>n</ci><cn type=""integer"">4</cn></apply></math>"
q_1030	A.101	3163489	question	"<?xml version='1.0' encoding='UTF-8'?>
<math xmlns=""http://www.w3.org/1998/Math/MathML""><ci>k</ci></math>"
q_1031	A.101	3163489	question	"<?xml version='1.0' encoding='UTF-8'?>
<math xmlns=""http://www.w3.org/1998/Math/MathML""><apply><eq/><ci>n</ci><ci>k</ci></apply></math>"
q_1032	A.101	3163489	question	"<?xml version='1.0' encoding='UTF-8'?>
<math xmlns=""http://www.w3.org/1998/Math/MathML""><apply><leq/><apply><csymbol>superscript</csymbol><ci>k</ci><cn type=""integer"">2</cn></apply><apply><csymbol>superscript</csymbol><cn type=""integer"">2</cn><ci>k</ci></apply></apply></math>"
q_1033	A.101	3163489	question	"<?xml version='1.0' encoding='UTF-8'?>
<math xmlns=""http://www.w3.org/1998/Math/MathML""><apply><leq/><apply><csymbol>superscript</csymbol><apply><plus/><ci>k</ci><cn type=""integer"">1</cn></apply><cn type=""integer"">2</cn></apply><apply><csymbol>superscript</csymbol><cn type=""integer"">2</cn><apply><plus/><ci>k</ci><cn type=""integer"">1</cn></apply></apply></apply></math>"
q_1034	A.101	3163489	question	"<?xml version='1.0' encoding='UTF-8'?>
<math xmlns=""http://www.w3.org/1998/Math/MathML""><apply><and/><apply><eq/><csymbol>absent</csymbol><apply><csymbol>superscript</csymbol><ci>k</ci><cn type=""integer"">2</cn></apply></apply><apply><leq/><apply><csymbol>superscript</csymbol><ci>k</ci><cn type=""integer"">2</cn></apply><apply><csymbol>superscript</csymbol><cn type=""integer"">2</cn><ci>k</ci></apply></apply></apply></math>"
q_1035	A.101	3163489	question	"<?xml version='1.0' encoding='UTF-8'?>
<math xmlns=""http://www.w3.org/1998/Math/MathML""><apply><and/><apply><eq/><csymbol>absent</csymbol><apply><times/><cn type=""integer"">2</cn><apply><csymbol>superscript</csymbol><ci>k</ci><cn type=""integer"">2</cn></apply></apply></apply><apply><leq/><apply><times/><cn type=""integer"">2</cn><apply><csymbol>superscript</csymbol><ci>k</ci><cn type=""integer"">2</cn></apply></apply><apply><csymbol>superscript</csymbol><cn type=""integer"">2</cn><apply><plus/><ci>k</ci><cn type=""integer"">1</cn></apply></apply></apply></apply></math>"
q_1036	A.101	3163489	question	"<?xml version='1.0' encoding='UTF-8'?>
<math xmlns=""http://www.w3.org/1998/Math/MathML""><apply><leq/><apply><csymbol>superscript</csymbol><apply><plus/><ci>k</ci><cn type=""integer"">1</cn></apply><cn type=""integer"">2</cn></apply><apply><times/><cn type=""integer"">2</cn><apply><csymbol>superscript</csymbol><ci>k</ci><cn type=""integer"">2</cn></apply></apply></apply></math>"
q_1037	A.101	3163489	question	"<?xml version='1.0' encoding='UTF-8'?>
<math xmlns=""http://www.w3.org/1998/Math/MathML""><apply><leq/><apply><csymbol>superscript</csymbol><apply><plus/><ci>k</ci><cn type=""integer"">1</cn></apply><cn type=""integer"">2</cn></apply><apply><csymbol>superscript</csymbol><cn type=""integer"">2</cn><apply><plus/><ci>k</ci><cn type=""integer"">1</cn></apply></apply></apply></math>"
q_1038	A.101	3163489	question	"<?xml version='1.0' encoding='UTF-8'?>
<math xmlns=""http://www.w3.org/1998/Math/MathML""><apply><times/><apply><csymbol>superscript</csymbol><apply><plus/><ci>k</ci><cn type=""integer"">1</cn></apply><cn type=""integer"">2</cn></apply><ci>≤</ci><cn type=""integer"">2</cn><apply><csymbol>superscript</csymbol><ci>k</ci><cn type=""integer"">2</cn></apply></apply></math>"
q_1039	A.101	3163489	question	"<?xml version='1.0' encoding='UTF-8'?>
<math xmlns=""http://www.w3.org/1998/Math/MathML""><apply><and/><apply><eq/><csymbol>absent</csymbol><apply><plus/><apply><csymbol>superscript</csymbol><ci>k</ci><cn type=""integer"">2</cn></apply><apply><times/><cn type=""integer"">2</cn><ci>k</ci></apply><cn type=""integer"">1</cn></apply></apply><apply><leq/><apply><plus/><apply><csymbol>superscript</csymbol><ci>k</ci><cn type=""integer"">2</cn></apply><apply><times/><cn type=""integer"">2</cn><ci>k</ci></apply><cn type=""integer"">1</cn></apply><apply><times/><cn type=""integer"">2</cn><apply><csymbol>superscript</csymbol><ci>k</ci><cn type=""integer"">2</cn></apply></apply></apply></apply></math>"
q_1040	A.101	3163489	question	"<?xml version='1.0' encoding='UTF-8'?>
<math xmlns=""http://www.w3.org/1998/Math/MathML""><apply><and/><apply><eq/><csymbol>absent</csymbol><apply><plus/><apply><times/><cn type=""integer"">2</cn><ci>k</ci></apply><cn type=""integer"">1</cn></apply></apply><apply><leq/><apply><plus/><apply><times/><cn type=""integer"">2</cn><ci>k</ci></apply><cn type=""integer"">1</cn></apply><apply><csymbol>superscript</csymbol><ci>k</ci><cn type=""integer"">2</cn></apply></apply></apply></math>"
q_1041	A.101	3163489	question	"<?xml version='1.0' encoding='UTF-8'?>
<math xmlns=""http://www.w3.org/1998/Math/MathML""><apply><and/><apply><eq/><csymbol>absent</csymbol><apply><plus/><apply><times/><cn type=""integer"">2</cn><ci>k</ci></apply><cn type=""integer"">1</cn></apply></apply><apply><leq/><apply><plus/><apply><times/><cn type=""integer"">2</cn><ci>k</ci></apply><cn type=""integer"">1</cn></apply><apply><csymbol>superscript</csymbol><cn type=""integer"">2</cn><ci>k</ci></apply></apply></apply></math>"
q_1042	A.101	3163489	question	"<?xml version='1.0' encoding='UTF-8'?>
<math xmlns=""http://www.w3.org/1998/Math/MathML""><apply><leq/><apply><csymbol>superscript</csymbol><apply><plus/><ci>k</ci><cn type=""integer"">1</cn></apply><cn type=""integer"">2</cn></apply><apply><times/><cn type=""integer"">2</cn><apply><csymbol>superscript</csymbol><ci>k</ci><cn type=""integer"">2</cn></apply></apply></apply></math>"
q_1043	A.101	3163489	question	"<?xml version='1.0' encoding='UTF-8'?>
<math xmlns=""http://www.w3.org/1998/Math/MathML""><apply><eq/><ci>n</ci><cn type=""integer"">4</cn></apply></math>"
q_1044	A.101	3163489	question	"<?xml version='1.0' encoding='UTF-8'?>
<math xmlns=""http://www.w3.org/1998/Math/MathML""><apply><eq/><list><ci>j</ci><ci>k</ci></list><ci>j</ci></apply></math>"
q_1045	A.101	3163489	question	"<?xml version='1.0' encoding='UTF-8'?>
<math xmlns=""http://www.w3.org/1998/Math/MathML""><apply><leq/><apply><plus/><apply><times/><cn type=""integer"">2</cn><ci>k</ci></apply><cn type=""integer"">1</cn></apply><apply><csymbol>superscript</csymbol><cn type=""integer"">2</cn><ci>k</ci></apply></apply></math>"