Tag Archives: Equations

Each of a+b,a+c,a+d,b+c,b+d,c+d,a+b+c+d is a square

    Find four distinct integers   a, b, c, d   such that a + b a + c a + d b + c b + d c + d a + b + c + d are … Continue reading

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Rational numbers (x,y); each of x – 1 and x + 1 is a square

    Solve,     Similarly for,     Solution: Put we get,     and                                      

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Each of a-b, a+n, b+n, a+b+n is a square

    To find two numbers,     and   ,   whose difference,     is a square and such that each,     and   ,   is a square and their sum,   ,   is a … Continue reading

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x^2 + y^6 = z^4

      ……………………………………………. …………………………………………….                                      

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x^2 + y^3 = z^4

      ……………………………………….. ………………………………………..     Related blog:   x^4 + y^3 = k*z^2, k is a small prime                            

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a^2 + a*b + b^2 and c^2 + c*d + d^2 … Part 3

      then,                                    

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a^4 + 2n(ab)^2 + b^4 = c^4 + 2n(cd)^2 + d^4 …. Part 2

    for   n = 1, 2, 3, …, 10     For   n = 11, 12, 13, …, 100                                                                         … Continue reading

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a^4 + 14(a*b)^2 + b^4 = c^4 + 14(c*d)^2 + d^4

    I like this type of equations, because they can be used to form identities.   Let’s solve for   n = 7 where     are distinct positive integers   For example,     Note that So,   … Continue reading

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(a^2 + b^2 + c^2 + d^2)(p^2 + q^2 + r^2 + s^2) — Part 3

          [ a sum of four squares] Or      [ as a sum of seven squares ]     Can you find positive integers     so that the expressions are to be made squares.       … Continue reading

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(a*p + b*q + c*r), (a*q – b*p), (a*r – c*p), (b*r – c*q) — Part 2

    Can you find positive integers     so that the expressions are to be made squares.     Note that                                     … Continue reading

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