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Weekly Challenge 43: A Close Match

Can you massage the parameters of these curves to make them match as closely as possible?

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Weekly Challenge 44: Prime Counter

A weekly challenge concerning prime numbers.

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Weekly Challenge 28: the Right Volume

Can you rotate a curve to make a volume of 1?

Weekly Challenge 31: Common Divisor

Stage: 5 Short Challenge Level: Challenge Level:1


Find the largest integer which divides every member of the following sequence: $$ 1^5-1,\ 2^5-2,\ 3^5-3,\cdots\ n^5-n.$$

Did you know ... ?

Although number theory - the study of the natural numbers - does not typically feature in school curricula it plays a leading role in university at first year and beyond. Having a good grasp of the fundamentals of number theory is useful across all disciplines of mathematics. Moreover, problems in number theory are a great leisure past time as many require only minimal knowledge of mathematical 'content'.