perplexus.info :: Numbers : Square of an Odd

Square of an Odd (Posted on 2002-10-06)

Take any odd number and square it. It will invariably be a multiple of 8 plus 1. So (odd)^2=8n+1 where n is an integer. Show why this is always so. Also show what the pattern for n is.

See The Solution Submitted by martyn

Rating: 3.1333 (15 votes)

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Subject	Author	Date
Puzzle Thoughts	K Sengupta	2023-09-15 08:45:41
Answer	Math Man	2013-06-10 16:51:54
Solution	Praneeth	2007-08-01 13:11:24
Puzzle solution ( Continued)	K Sengupta	2007-04-20 12:23:11
Puzzle solution	K Sengupta	2007-04-20 12:16:21
sol	Andre	2005-09-07 22:03:39
hmm..	Amon	2005-05-04 02:46:33
Similar problem	Jonathan Fletcher	2004-10-07 07:32:51
im smart	Billy Bob	2004-03-25 13:05:15
induction does it	Ady TZIDON	2004-03-04 03:30:15
a simple solution	red_sox_fan_032003	2004-03-03 17:56:18
Part 1,The formula for n	Tim Axoy	2003-03-26 02:24:55
Part 1,The odd number 2m+1	Tim Axoy	2003-03-26 02:19:24
re: Alternate Approach	Gamer	2003-03-12 14:06:00
Not factorial!	TomM	2002-10-07 19:16:26
Square of an Odd Number	Douglas Johnson	2002-10-07 15:47:22
Answer to first question	Dulanjana	2002-10-07 14:46:57
Alternate Approach	TomM	2002-10-06 17:52:23
re: no solution?	TomM	2002-10-06 17:33:36
no solution?	martyn	2002-10-06 17:19:53
Heh!	TomM	2002-10-06 13:25:45

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