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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
2 months, 1 week ago

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