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 

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


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


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