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\[\large 1+\frac { 1 }{ 5 } +\frac { 1\times 3 }{ 5\times 10 } +\frac { 1\times 3\times 5 }{ 5\times 10\times 15 } + \ldots \]

If the square of the series ...

\[\dfrac{y}{x^{2}+1} + \dfrac{x}{y^{2}+1}\]

If \(x= \sqrt{3} + \sqrt{2}\) and \(y= \sqrt{3} - \sqrt{2}\), then the expression above can be simplified to ...

Let \(p\), \(q\) and \(r\) be prime numbers such that

\[pqr=19(p+q+r).\]

What is the value of \(p^2+q^2+r^2\)?

Find the integer value of \(n\) such that \(2^{200}-(2^{192} \times 31)+2^n\) is a perfect square.

Find the number of perfect square divisors of \(12!\).

Clarification: It is 12 factorial. That is, \(12 \times 11 \times 10 \times \ldots \times 2 \times 1 \).

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