Tag Archives: Number theory

Maths prize: casting out nines

The first ever printed maths book, as far as we know, was the “Treviso Arithmetic”, printed in Treviso, near Venice, in Italy, in 1478. A printed edition of Euclid’s “Elements” came out soon after, in 1482. Unlike Euclid, where everything is proofs, the Treviso Arithmetic was a collection of practical ideas to do or check calculations.

castoutnines Continue reading

Fortnightly maths prize for 23 June

No-one attempted this one, which I guess is due to it being post-exam time rather than it being specially difficult.

Part 1:

image

To help you: 1+2+3+4+….+n=┬Żn(n+1) for all n

Part 2:

Find the sum to n terms of the first n numbers multiplied pairwise

For n = 3 it is 1×2 + 1×3 + 2×3, which makes 11

Your job is to find a general formula which works for any n.

To help you: 12+22+32+….+n2=16n(n+1)(2n+1). Continue reading