Out of the dates given below which date constitutes a Pythagorean triplet?
A.\[15/08/17\]
B.\[16/08/16\]
C.\[3/5/17\]
D.\[4/9/15\]

Hint: First we have to define what the terms we need to solve the problem are.
In the given dates, we need to find whether it constitutes a Pythagorean triplet or not. We can find this by knowing some concepts about the Pythagorean triplet. By applying the Pythagorean triplet condition we can find it. Pythagorean triples are the three positive integers that completely satisfy Pythagoras theorem
Formula to be used:
A Pythagorean triplet consists of three positive integers\[a\], \[b\] and\[c\], such that\[{a^2} + {b^2} = {c^2}\]..

Complete step by step answer:
Explaining option A) \[15/08/17\]
\[a = 15,b = 8,c = 17\]
\[{a^2} + {b^2} = {c^2}\]
Substituting the values of \[a,b,c\] in the formula
\[{15^2} + {8^2} = {17^2}\]
\[225 + 64 = 289\]
\[289 = 289\]
The values are equal.It satisfies the condition.
The date \[15/08/17\] satisfies the Pythagorean triplet condition.
Hence it is a Pythagorean triplet.
Explaining option B) \[16/08/16\]
\[a = 16,b = 8,c = 16\]
\[{a^2} + {b^2} = {c^2}\]
Substituting the values of \[a,b,c\] in the formula
\[{16^2} + {8^2} = {16^2}\]
\[256 + 64 = 256\]
\[320 \ne 256\]
The values are not equal. It does not satisfy the condition.
The date \[16/08/16\]does not satisfy the Pythagorean triplet condition.
Hence it is not a Pythagorean triplet
Explaining option C) \[3/5/17\]
\[a = 3,b = 5,c = 17\]
Substituting the values of \[a,b,c\] in the formula
\[{a^2} + {b^2} = {c^2}\]
\[{3^2} + {5^2} = {17^2}\]
\[9 + 25 = 289\]
\[34 \ne 289\]
The values are not equal. It does not satisfy the condition.
The date \[3/5/17\]does not satisfy the Pythagorean triplet condition.
Hence it is not a Pythagorean triplet
Explaining option D) \[4/9/15\]
\[a = 4,b = 9,c = 15\]
\[{a^2} + {b^2} = {c^2}\]
Substituting the values of \[a,b,c\] in the formula
\[{4^2} + {9^2} = {15^2}\]
\[16 + 81 = 225\]
\[97 \ne 225\]
The values are not equal. It does not satisfy the condition.
The date \[3/5/17\]does not satisfy the Pythagorean triplet condition.
Hence it is not a Pythagorean triplet

The correct option is A) \[15/08/17\]

Note:
Pythagoras who was a mathematician was interested in mathematics, science and philosophy.
He is famous for the property of triangles with a right angle \[{90^0}\].
An interesting fact about the Pythagorean triples is that Pythagorean triple always consists of all even numbers or two odd numbers and an even number
Pythagoras made important development in mathematics and astronomy.