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Puzzles
121
Source:
Mathematical Circus
by Martin Gardner
Find a number base other than 10 in which 121 is a perfect square.
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This is true for any base larger than 2. This is because:
$$121_n = 1+2n+n^2$$ $$=(n+1)^1$$
Extension
Which other base 10 square numbers are always square in high enough bases?
Tags:
numbers
,
bases
If you enjoyed this puzzle, check out
Sunday Afternoon Maths XLIV
,
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, or
a random puzzle
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number
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books
symmetry
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axes
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coins
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pascal's triangle
matrices
quadrilaterals
speed
folding tube maps
digits
cubics
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multiplication
integration
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albgebra
menace
shapes
prime numbers
clocks
circles
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chalkdust crossnumber
3d shapes
doubling
perfect numbers
money
even numbers
square roots
sport
perimeter
fractions
people maths
expansions
numbers
binary
mean
polygons
the only crossnumber
geometry
cube numbers
advent
regular shapes
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differentiation
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remainders
decahedra
bases
ellipses
tiling
dates
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scales
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elections
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median
consecutive numbers
angles
cryptic crossnumbers
tangents
parabolas
planes
floors
products
shape
combinatorics
sequences
dominos
taxicab geometry
division
proportion
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determinants
crossnumber
complex numbers
rugby
consecutive integers
christmas
partitions
algebra
squares
area
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addition
surds
coordinates
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multiples
time
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functions
ave
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