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


Show me a random puzzle
 Most recent collections 

Sunday Afternoon Maths LXVII

Coloured weights
Not Roman numerals

Advent calendar 2018

Sunday Afternoon Maths LXVI

Cryptic crossnumber #2

Sunday Afternoon Maths LXV

Cryptic crossnumber #1
Breaking Chocolate
Square and cube endings

List of all puzzles


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


Show me a random puzzle
▼ show ▼
© Matthew Scroggs 2019