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 A^2 = B^3 + C^3
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 smallest integer whose first n multiples all contain a 3
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Monthly Archives: February 2014
Puzzle: Sum of the factorials of the digits of an Integer N
To find integers N such that the sum of the factorials of the digits of N is equal to the reversal of its largest prime factor. In the first example, 143 = 11 X … Continue reading
(a/(a+b))^2 + b/(a+b) = (b/(a+b))^2 + a/(a+b)
Can you find other examples?
Puzzle : Acute Triangles – Area is 4 times the perimeter
Find all the acute triangles whose sides are integers and whose area is 4 times its perimeter. —————————————— Puzzle #1 Paul found: Obtuse and Right triangles : —————————————— Puzzle … Continue reading
Positive integers (a,b,c); a^2 – a*b + b^2 = c^2
Here are few examples: Find more examples.
The sum of the first n natural numbers and other sums
@grey_matter noticed a pattern with Pascal’s triangle —————————————— #2 —————————————— #3 —————————————— #4 Paul adds: … Continue reading
Triangle whose angles are 15, 55, 110
How Euler Did It http://eulerarchive.maa.org/hedi/HEDI200404.pdf
Repunits and Repdigits  x + y^2 = z
A repunit is a number consisting of copies of the single digit 1. repunits have the form (10^n – 1)/9 Repunit http://mathworld.wolfram.com/Repunit.html http://en.wikipedia.org/wiki/Repunit Repdigit http://mathworld.wolfram.com/Repdigit.html http://en.wikipedia.org/wiki/Repdigit Prove that the pattern continues. @ChrisMaslanka solved … Continue reading
Four Rectangles, 2 Squares
Solution: Abdul Hafiz Kaissi answered correctly