Pythagorean Independence Day

Today is 15th August 2017. The 70th anniversary of the Independence Day of India. .

The date has an interesting property. 15th August 2017 is written as 15/8/17 in India. (It is written as 8/15/17 in American style. But, I am not concerned about that. Nor would that affect the mathematical beauty of the date)

It can be noticed here that in 15/8/17, \(15^2+8^2=17^2\). The triplet is a Pythagorean Triplet.

I had never realized that the Indian Independence Day date has the property of being a part of a Pythagorean Triplet.

Now the question comes : How common or rare are the dates in the calendar which can be part of a Pythagorean Triplet?

As it turns out, they are indeed rare.

There are only 12 dates (dd/mm/yy) which have the property \(dd^2+mm^2=yy^2\)

04/03/05, 03/04/05, 12/05/13, 08/06/10, 24/07/25, 06/08/10, 15/08/17, 12/09/15, 24/10/26, 05/12/13, 09/12/15, 16/12/20

If one relaxes the condition that \((dd,mm,yy)\) form a pythagorean triplet without the restriction that \(yy\) is the largest number in the triplet, 16 additional dates would arise.

05/03/04, 05/04/03, 03/05/04, 04/05/03, 13/05/12, 10/06/08, 25/07/24, 10/08/06, 17/08/15, 15/09/12, 06/10/08, 08/10/06, 26/10/24, 13/12/05, 15/12/09, 20/12/16

Now, my fellow mathematical enthusiasts can see if any of the above dates are relevant to them and spread the word of the speciality of that date

Note by Janardhanan Sivaramakrishnan
11 months ago

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This is awesome!!!!!!!!!!!!!

Sumukh Bansal - 7 months, 1 week ago

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