mscroggs.co.uk
mscroggs.co.uk
Click here to win prizes by solving the mscroggs.co.uk puzzle Advent calendar.
Click here to win prizes by solving the mscroggs.co.uk puzzle Advent calendar.

subscribe

Puzzles

3n+1

Let \(S=\{3n+1:n\in\mathbb{N}\}\) be the set of numbers one more than a multiple of three.
(i) Show that \(S\) is closed under multiplication.
ie. Show that if \(a,b\in S\) then \(a\times b\in S\).
Let \(p\in S\) be irreducible if \(p\not=1\) and the only factors of \(p\) in \(S\) are \(1\) and \(p\). (This is equivalent to the most commonly given definition of prime.)
(ii) Can each number in \(S\) be uniquely factorised into irreducibles?

Show answer & extension

Archive

Show me a random puzzle
 Most recent collections 

Advent calendar 2019

Sunday Afternoon Maths LXVII

Coloured weights
Not Roman numerals

Advent calendar 2018

Sunday Afternoon Maths LXVI

Cryptic crossnumber #2

List of all puzzles

Tags

rugby number menace time unit fractions books games christmas chalkdust crossnumber lines triangles surds irreducible numbers crosswords partitions complex numbers circles planes floors digital clocks multiples cryptic clues proportion sums crossnumber logic coins advent sum to infinity people maths dates cryptic crossnumbers cube numbers quadratics indices perimeter colouring remainders routes integration differentiation functions crossnumbers wordplay palindromes angles trigonometry addition volume hexagons mean median grids graphs the only crossnumber cards 2d shapes percentages spheres shapes clocks factorials square numbers balancing integers scales sequences squares odd numbers elections probability triangle numbers multiplication speed rectangles prime numbers arrows doubling averages dominos digits numbers calculus square roots tiling range dodecagons fractions bases area polygons ave taxicab geometry ellipses 3d shapes regular shapes geometry symmetry division means chocolate pascal's triangle sport folding tube maps dice algebra money probabilty coordinates factors shape gerrymandering perfect numbers parabolas chess products star numbers

Archive

Show me a random puzzle
▼ show ▼
© Matthew Scroggs 2012–2020