Monthly Archives: November 2014

Pythagorean triples – (a+x)^2 + (b+y)^2 ≤ (c+z)^2

  (a, b, c)   and   (x, y, z)   are Pythagorean triples. Prove that                      Determine when equality holds                           Advertisements

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Primitive Pythagorean triples – shortest leg is odd

    The table shows that all the primitive Pythagorean triples with   c ≤ 300,   and a is odd. (c-a)/2,   (c+a)/2,   c+b,   c-b   are all perfect squares   Prove that if   (a, b, … Continue reading

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Primitive Pythagorean triples – odd integers

  Previous posts: Primitive Pythagorean triples with inradius from 1 to 250 Prove that In all Pythagorean triangles, the inradius is a whole number. The number of primitive Pythagorean triangle with a fixed inradius is always a power of 2. … Continue reading

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Num3er 38

    38 has 4 divisors:     1     2     19     38 Sum of divisors:     60 38   is a semiprime 38   =   2   *   19   sum of consecutive numbers: 38 = 8 … Continue reading

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Primitive Pythagorean triples – polynomials: x^2 + px ± q

  If   p and   q be relatively prime integers,   gcd(p,q) = 1 The polynomials     are both factorable (over integers) if and only if |p| and |q| are respectively the hypotenuse and area of a primitive … Continue reading

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All Primitive Pythagorean triples with Palindromic Perimeter < 10^6

                               

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(cos x + sin x)/(cos x – sin x) = tan N

      Paul found the sequence:    6 * 19,    6 * 49,    6 * 79,    6 * 109,                          

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All Pythagorean triples with Palindromic Perimeter ≤ 89998

  All Pythagorean triples with Palindromic Perimeter ≤ 69996                              

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All Pythagorean triples with Palindromic Perimeter ≤ 69996

  All Pythagorean triples with Palindromic Perimeter < 49994                          

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a^2 b^2 + b^2 c^2 + c^2 a^2 = d^2

    such that   a, b, c, d   are integers and   gcd(a,b,c) = 1   For example,                                                   Find more solutions.                     … Continue reading

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