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October 13th, 2017, 06:10 AM  #1 
Newbie Joined: Oct 2017 From: Norway Posts: 3 Thanks: 0  Nice date properties (equation system?)
Hi there, I recently came across some cool properties when I analyzed my birth date. 21/02/1998 21·02 = 42 19·98 = 1862; √(1862) = 43.150898… 2102+1998 = 4100 This is pretty close but not quite there. So in general I wanted to find a date of the format DD/MM/YYYY which fulfills these properties: DD·MM=x YY·YY=x² DDMM+YYYY=100x I'm not the best in mathematics so I didn't find a date but couldn't disprove that one exists as well. I'm really curious if somebody can find a date where these properties are valid. Have a nice day BGH 
October 13th, 2017, 07:38 AM  #2 
Global Moderator Joined: Dec 2006 Posts: 18,142 Thanks: 1416 
I think the "closest" dates are 18/04/5496 and 21/02/1898.

October 13th, 2017, 08:06 AM  #3 
Math Team Joined: Jan 2015 From: Alabama Posts: 2,820 Thanks: 750 
Hmmm already missed one, gonna have to wait a long time for the other!

October 13th, 2017, 08:55 AM  #4 
Newbie Joined: Oct 2017 From: Norway Posts: 3 Thanks: 0  I have found the dates 21/03/4197 and 13/06/6495 which are extremely close: 21/03/4197 21*03 = 63 41*97 = 3977 instead of 63² = 3969 2103+4197 = 6300 13.06.6495 13*6 = 78 64*95 = 6084 instead of 18² = 6080 1306+6495 = 7801 instead of 7800 There might be no real solution though unfortunately. 
October 13th, 2017, 01:51 PM  #5 
Global Moderator Joined: Dec 2006 Posts: 18,142 Thanks: 1416 
I assume you meant "64*95 = 6080 instead of 78² = 6084". There's also 08/10/7190: 08*10 = 80 71*90 = 6390, instead of 80² = 6400 0810 + 7190 = 8000 
October 14th, 2017, 10:37 AM  #6 
Senior Member Joined: Sep 2016 From: USA Posts: 196 Thanks: 103 Math Focus: Dynamical systems, analytic function theory, numerics 
There are no solutions. If $DM = x$ and $DM + Y = 100x$ then $x + Y = 100x$ which requires $Y = 99x$. Apply to the 2nd equation yields $Y^2 = x^2 = 99^2x^2$ requiring $x = 0$. 
October 16th, 2017, 12:11 PM  #7  
Newbie Joined: Oct 2017 From: Norway Posts: 3 Thanks: 0  Quote:
f.e. 12.01.2015 DM = 12*1 = 12 DM + Y = 1201+1000 = 2201  

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