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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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 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: June 2013
Sum of four consecutive cubes is a square
(x – 1)^3 + x^3 + (x + 1)^3 + (x + 2)^3 = 4*x^3 + 6*x^2 + 18*x + 8 we want this sum … Continue reading
Sum of two Triangular Numbers
Definition: http://mathworld.wolfram.com/TriangularNumber.html Let T(1) and T(2) be two triangular numbers T(1) = (a^2 + a)/2 T(2) = (b^2 + b)/2 Let n be the sum n = (a^2 + a)/2 + … Continue reading
Primes in a Circle
Place the numbers 1 to 14 around a circle so that both the sum and the (positive difference) of any two neighboring numbers is a prime. Source: wordplay.blogs.nytimes
Patterns  Perfect Num3ers in bases 2, 3, 4
A perfect number is a positive integer that is equal to the sum of its proper positive divisors. http://mathworld.wolfram.com/PerfectNumber.html in base 10: 6 28 496 8128 33550336 8589869056 137438691328 2305843008139952128 2658455991569831744654692615953842176 191561942608236107294793378084303638130997321548169216 Note the patterns, when … Continue reading
Num3er 2013  N^2 = a^3 + b^3 + c^3 – 3abc
N^2 = a^3 + b^3 + c^3 – 3abc 2013^2 = (714)^3 + 100^3 + 617^3 – 3(714)(100)(617) 2013^2 = … Continue reading
Logic puzzle #Mensa  Card puzzle
Puzzle: Each card has a letter (consonant or vowel) on one side, and a number (odd or even) on the other side. Rule: If there’s a vowel on one side of the card, there’s always an odd number on the … Continue reading
Palindromic primes  Equalities
Prime numbers under 1000: 2, 3, 5, 7, 11, 13, 17, 19, 23, 29, 31, 37, 41, 43, 47, 53, 59, 61, 67, 71, 73, 79, 83, 89, 97, 101, 103, 107, 109, 113, 127, 131, 137, 139, 149, 151, … Continue reading
Posted in Math Beauty, Number Puzzles
Tagged Equalities, Palindromic primes, Prime Numbers
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Pattern  Num3er 84
84 can be expressed as a sum of 8 consecutive numbers in descending order: 84 = 14 + 13 + 12 + 11 + 10 + 9 + 8 + 7 and 14 + 13 + 12 … Continue reading
Num3er 162
Pat’s blog asks: 162 is the smallest number that can be written as the sum of 4 positive squares in 9 ways. Can you find all nine ways? 162 can be expressed as the sum of … Continue reading
Multiplication puzzle #2
Older post: Multiplication puzzle #1 In this multiplication, each digit from 09 appears exactly 2 times. N.B. No leading zeros in any number. ? ? ? * ? ? ? ———– … Continue reading