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 October 13th, 2017, 05:10 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, 06:38 AM #2 Global Moderator   Joined: Dec 2006 Posts: 21,036 Thanks: 2273 I think the "closest" dates are 18/04/5496 and 21/02/1898.
 October 13th, 2017, 07:06 AM #3 Math Team   Joined: Jan 2015 From: Alabama Posts: 3,264 Thanks: 902 Hmmm- already missed one, gonna have to wait a long time for the other!
October 13th, 2017, 07:55 AM   #4
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Quote:
 Originally Posted by skipjack I think the "closest" dates are 18/04/5496 and 21/02/1898.
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, 12:51 PM #5 Global Moderator   Joined: Dec 2006 Posts: 21,036 Thanks: 2273 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, 09:37 AM #6 Senior Member   Joined: Sep 2016 From: USA Posts: 670 Thanks: 440 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, 11:11 AM   #7
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Quote:
 Originally Posted by SDK 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 $x = 0$.
But in the equation DM = x, DM is meant to be D*M whereas in DM + Y, DM is the number DM itself.

f.e.
12.01.2015
DM = 12*1 = 12
DM + Y = 1201+1000 = 2201

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