Monthly Archives: August 2015

Find (x,y) so that (x+1)/y + (y+1)/x is a positive integer

  You may want to prove the last statement.                                 Advertisements

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Solutions to x^2 ± x*y + y^2 = z^2

  Solutions to       when     is an odd integer     Generalize this.                                  

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Open question: Positive integers as a sum of squares and cubes?

    Every positive integer is a sum of four squares (Lagrange’s Theorem) It is known that every positive integer is a sum of no more than 9 positive cubes, and that every “sufficiently large” integer is a sum of … Continue reading

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Puzzle | ArithmeticMean() and HarmonicMean()

    Let’s take the number   10 10   has   4   divisors:      1   2   5   10 Let’s compute the Arithmetic Mean and Harmonic Mean of   (1, 2, 5, 10) Multiplying the two means: … Continue reading

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floor(√x – √y) = floor(√17) where (x,y) are prime numbers

  Here are solutions for   y   =   2,   3,   5,   7                                

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Can you find a triangular number with exactly 500 divisors?

    is the smallest triangular number which has 576 divisors   Can you find a triangular number with exactly 500 divisors?                                  

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Diophantine Equation| x^3 + y^3 + z^3 – 3 xyz = A^3

    Case #1 : ,       ,       ,      and ,           Here are the first few examples:     Case #2 : ,       ,       ,     and ,          Here are the first … Continue reading

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Number of divisors: d(a)=8, d(b)=18 and b-a=28 (sequence:8,18,28)

    Let     be the number of divisors of   Find positive integers     such that    and    and      the smallest pair that satisfies the two conditions are   (152, 180) : 152   … Continue reading

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Documentary | Decoding the Universe: The Great Math Mystery

                                         

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Puzzle| Digit Permutations of 123,1234,12345,123456,…

    By permuting the digits of the number   123,   we obtain 6 different numbers: 123,   132,   213,   231,   312,   321 The sum of these numbers is : 123   +   132 … Continue reading

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