Solve in integer numbers

• December 19th 2010, 01:18 PM
oszust001
Solve in integer numbers
How to solve that eqation?
$3^x=4y+5$
• December 19th 2010, 01:19 PM
dwsmith
$3^x\equiv 5=1 \ \mbox{(mod 4)}$
• December 19th 2010, 01:25 PM
oszust001
Ok, but what it is. How can I do i to my equation.
• December 19th 2010, 01:26 PM
dwsmith
What happens when x = 2? How about x = 4? ....
• December 19th 2010, 01:28 PM
oszust001
Can you solve me a complete this equation, Step by step?
• December 19th 2010, 01:37 PM
dwsmith
I pretty much solved it for you already.

When x = 2, the congruence is true.

When x = 4, it is true.

x = 6, true as well.

x = 8 guess what? True.

Notice anything?

Let's not forgot x = 0 is true too.
• December 19th 2010, 01:46 PM
emakarov
$3^{2k}=9^k\equiv 1^k=1\pmod{4}$, but $3^{2k+1}=9^k\cdot 3\equiv 3\pmod{4}$.
{"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": 4, "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": 0.49309828877449036, "perplexity": 3778.216008813135}, "config": {"markdown_headings": false, "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-2013-48/segments/1387345775355/warc/CC-MAIN-20131218054935-00050-ip-10-33-133-15.ec2.internal.warc.gz"}