Sunday Afternoon Maths XVII

 Posted on 2014-06-15 

Differentiate this

$$f(x)=e^{x^{ \frac{\ln{\left(\ln{x}\right)}}{ \ln{x}}} }$$
Find \(f'(x)\).

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Square numbers

Towards the end of his life, Lewis Carroll recorded in his diary that he had discovered that double the sum of two square numbers could always be written as the sum of two square numbers. For example
$$2(3^2 +4^2 )=1^2 +7^2$$ $$2(5^2 +8^2 )=3^2 +13^2$$
Prove that this can be done for any two square numbers.

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Consider three-digit integers \(N\) such that:
(a) \(N\) is not exactly divisible by 2, 3 or 5.
(b) No digit of \(N\) is exactly divisible by 2, 3 or 5.
How many such integers \(N\) are there?

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Maths Jam is always held on the second-to-last Tuesday of the month. This month, it will be held on the 17th. What is the earliest date in the month on which Maths Jam can fall and when will this next happen?

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Tags: dates
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