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 2020

Advent calendar 2019

Sunday Afternoon Maths LXVII

Coloured weights
Not Roman numerals

Advent calendar 2018


List of all puzzles

Tags

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

Archive

Show me a random puzzle
▼ show ▼
© Matthew Scroggs 2012–2021