Monthly Archives: April 2016

Sums & Products| x+y+z=a+b+c and x*y*z=a*b*c

  Note that 118 can be partitioned into three parts that have the same product in 4 different ways:     and It is the smallest number for which that is possible. Find the next smallest one.                                    ***************************************************** … Continue reading

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When x ± y, x ± z, y ± z are squares

    Find positive integers     so that the expressions are to made squares.   Here are some solutions:   ,      ,        ,      ,        ,     ,     ,     ,     , … Continue reading

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Pythagorean triples – Equal products of two legs and hypotenuse?

    The following integers define two right triangles   ,     Can you find a pair of Pythagorean triples with equal products of two legs and hypotenuse:   Is it possible to find a pair of primitive Pythagorean … Continue reading

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Pythagorean triples – Equal products of two legs

    The following integers define two right triangles   ,     Can you find a pair of Pythagorean triples with equal products of two legs:     Related blog:   Pythagorean triples – Equal products of a leg … Continue reading

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Primitive Pythagorean triples: Pandigital Areas

      Paul found all the 10-digit pandigital area PPT: 1458376920    {39760,   73359,   83441} 1476958230    {6660,   443531,   443581} 1498637250    {39699,   75500,   85301} 1547836290    {37765,   81972,   90253} 1567984320 … Continue reading

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When a*b*x*y and (a^2 + b^2)(x^2 + y^2) are both squares

        Here’s one possible solution: (15,   112,   113),   a Primitive Pythagorean triple, and (12,   35,   37),   also a Primitive Pythagorean triple. a = 15,   b = 112,      x = … Continue reading

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a^2+b^2, a^2+c^2, b^2+c^2

      Here are the parametric equations: where     is a Pythagorean triple                                  

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a^2+b^2+c^2, a^2+b^2+d^2, a^2+c^2+d^2, b^2+c^2+d^2

    To find positive integers   a,   b,   c,   and   d   such that     Here’s a couple of examples if we let   a = d a = 120,    b = 28, … Continue reading

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Claim: True or False. How a prime can be obtained.

    Prove or disprove the following claim: From every odd integer, a prime can be obtained by adding to it or by subtracting from it a suitable power of 2.                   … Continue reading

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Palindrome 2662

      We may partition the palindrome 2662 into two integers, one of which is divisible by 29 and the other by 43.   29, 31, 41, 43   are prime numbers 29 and 31 form a twin prime … Continue reading

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