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 A^2 = B^3 + C^3
 Set {4,b,c,d,e} such that the product of any two of them increased by 1 is a square
 smallest integer whose first n multiples all contain a 3
 Set {3,b,c,d,e} such that the product of any two of them increased by 1 is a square
 Set {2,b,c,d,e} such that the product of any two of them increased by 1 is a square
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Monthly Archives: April 2013
#puzzle  Base 9 — Part 3
Note the pattern: Base 9 Base 10 210 … Continue reading
#Puzzle  Bases less than 10 – digit reversals — Part 2
Find, for each base system less than 10 (bases 2 to 9), every instance of a number formed of two different nonzero digits that is a multiple of the number obtained by interchanging the digits. … Continue reading
#Puzzle  Base 7 — (Part 1)
There’s a unique 4digit number in base 10 that can be converted into its equivalent in base 7 by interchanging the left hand and right hand digit pairs. Find it. @mikeandallie and @InfinitelyManic : 1234 … Continue reading
lcm(a,b,c,d) = a+b+c+d
Definition: Least common multiple http://en.wikipedia.org/wiki/Least_common_multiple http://mathworld.wolfram.com/LeastCommonMultiple.html —————————————— Goal: To find four positive integers a, b, c, d such that LCM (a, b, c, d) = a + b + c + d Irreducible … Continue reading
Powers  5^n
n 5^n 1 5 2 25 3 125 4 … Continue reading
Num3ers of the form 3^n – 2^n
“Why are numbers beautiful? It’s like asking why is Beethoven’s Ninth Symphony beautiful. If you don’t see why, someone can’t tell you. I know numbers are beautiful. If they aren’t beautiful, nothing is.” ~ Paul Erdös —————————————— … Continue reading
Posted in Math Beauty, Number Puzzles
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Concatenation  Appending and Prepending the digits 1 and 3 to a string
17 —–> 1173 1173 ——– = 69 17 59 —–> 1593 1593 ——— = 27 59 769231 —–> 17692313 17692313 —————– = 23 769231 … Continue reading
Common digits : N and N^2
The smallest integers N, such that N and N^2 share the same digits are: 1 digit in common : 5^2 = 25 6^2 = 36 2 common digits : 11^2 = 121 25^2 … Continue reading
Odd Num3ers less than 100 in base 11
Take an odd number less than 100 and multiply it by 95 95 * 1 = 95 95 * 3 = 285 95 * 5 = 475 95 * 7 = 665 95 * 9 = 855 95 * 11 … Continue reading