# Sunday Afternoon Maths LIII

**Posted on 2016-05-29**

## Lots of ones

Is any of the numbers 11, 111, 1111, 11111, ... a square number?

## An integral

Source: Alex Bolton (inspired by Book Proofs blog)

What is

$$\int_0^{\frac\pi2}\frac1{1+\tan^a(x)}\,dx?$$
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Is any of the numbers 11, 111, 1111, 11111, ... a square number?

Source: Alex Bolton (inspired by Book Proofs blog)

What is

$$\int_0^{\frac\pi2}\frac1{1+\tan^a(x)}\,dx?$$
Not Roman numerals

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