mscroggs.co.uk
mscroggs.co.uk

subscribe

Puzzles

Square numbers

Towards the end of his life, Lewis Carroll recorded in his diary that he had discovered that double the sum of two square numbers could always be written as the sum of two square numbers. For example
$$2(3^2 +4^2 )=1^2 +7^2$$ $$2(5^2 +8^2 )=3^2 +13^2$$
Prove that this can be done for any two square numbers.

Show answer & extension

If you enjoyed this puzzle, check out Sunday Afternoon Maths XVII,
puzzles about square numbers, or a random puzzle.

Archive

Show me a random puzzle
 Most recent collections 

Advent calendar 2024

Advent calendar 2023

Advent calendar 2022

Advent calendar 2021


List of all puzzles

Tags

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

Archive

Show me a random puzzle
▼ show ▼
© Matthew Scroggs 2012–2025