# Math Help - Contradiction proof

2. ok, e n is odd and $n^3$ is even. By def of odd and even, there
$\exists \: m \in \mathbb{Z}$ such that $n = 2m + 1$ similarly, $\exists \: k \in \mathbb{Z}$ such that $n^3 = 2k$ so $(2m+1)^3 = 2k$ if you remember what division meant, if a divides b then there exists an integer g such that b = ag. since k is an integer, this means 2 divides (2m+1)^3 which means 2 divides (2m+1) which is a contradiction.
{"extraction_info": {"found_math": true, "script_math_tex": 0, "script_math_asciimath": 0, "math_annotations": 0, "math_alttext": 0, "mathml": 0, "mathjax_tag": 0, "mathjax_inline_tex": 0, "mathjax_display_tex": 0, "mathjax_asciimath": 0, "img_math": 0, "codecogs_latex": 6, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0, "katex": 0, "math-container": 0, "wp-katex-eq": 0, "align": 0, "equation": 0, "x-ck12": 0, "texerror": 0, "math_score": 0.9238120913505554, "perplexity": 372.9589173534621}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.18, "absolute_threshold": 10, "end_threshold": 15, "enable": true}, "remove_buttons": true, "remove_image_figures": true, "remove_link_clusters": true, "table_config": {"min_rows": 2, "min_cols": 3, "format": "plain"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "warc_path": "s3://commoncrawl/crawl-data/CC-MAIN-2014-35/segments/1408500823634.2/warc/CC-MAIN-20140820021343-00213-ip-10-180-136-8.ec2.internal.warc.gz"}