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Find the sum, f(n), of the first n terms of the sequence: 0, 1, 1, 2, 2, 3, 3........p, p, p +1, p + 1,..... Prove that f(a + b) - f(a - b) = ab.
Peter Zimmerman, a Year 13 student at Mill Hill County High School in Barnet, London wrote this account of modulus arithmetic.
Is this a fair game? How many ways are there of creating a fair game by adding odd and even numbers?
Investigate powers of numbers of the form (1 + sqrt 2).
In this 7-sandwich: 7 1 3 1 6 4 3 5 7 2 4 6 2 5 there are 7 numbers between the 7s, 6 between the 6s etc. The article shows which values of n can make n-sandwiches and which cannot.
Use algebra to reason why 16 and 32 are impossible to create as the sum of consecutive numbers.
Follow-up to the February Game Rules of FEMTO.
A new card game for two players.
Why are there only a few lattice points on a hyperbola and infinitely many on a parabola?
Which of these continued fractions is bigger and why?