mscroggs.co.uk
mscroggs.co.uk

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

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

Archive

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