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October 13th, 2017, 06:10 AM   #1
bgh
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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
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October 13th, 2017, 07:38 AM   #2
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I think the "closest" dates are 18/04/5496 and 21/02/1898.
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October 13th, 2017, 08:06 AM   #3
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Hmmm- already missed one, gonna have to wait a long time for the other!
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October 13th, 2017, 08:55 AM   #4
bgh
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Quote:
Originally Posted by skipjack View Post
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.
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October 13th, 2017, 01:51 PM   #5
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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
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October 14th, 2017, 10:37 AM   #6
SDK
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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 $x = 0$.
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October 16th, 2017, 12:11 PM   #7
bgh
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Quote:
Originally Posted by SDK View Post
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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