# Thread:

1. ## Need help doing a proof

Prove:
If a positive integer n is not prime, then 2^(n)-1 is not prime.

If n is not prime, then it factors into n = a*b. Use the identity
x^(b) = (x-1)(x^(b-1) + x^(b-2) + ...+ x + 1) and substitute x = 2^(a).

2. Originally Posted by noles2188
Prove:
If a positive integer n is not prime, then 2^(n)-1 is not prime.

If n is not prime, then it factors into n = a*b. Use the identity
x^(b) = (x-1)(x^(b-1) + x^(b-2) + ...+ x + 1) and substitute x = 2^(a).
There's a "-1" missing in that identity. It should be $x^b {\color{red}{} - 1} = (x-1)(x^{b-1} + x^{b-2} + \ldots + x + 1)$. Substitute $x=2^a$ in that and you should have no trouble getting the result.
{"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": 2, "wp_latex": 0, "mimetex.cgi": 0, "/images/math/codecogs": 0, "mathtex.cgi": 0}, "config": {"markdown_headings": true, "markdown_code": true, "boilerplate_config": {"ratio_threshold": 0.3, "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": "github"}, "remove_chinese": true, "remove_edit_buttons": true, "extract_latex": true}, "english_confidence": 0.8316499590873718, "perplexity_flag": "middle"}