Category Archives: Uncategorized

What is the number of the parking space?

        Source:   Hong Kong elementary school                                              

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Which of the following two numbers is larger

                                               

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Pythagorean triangles – Area + shortest leg is a square

    Find Pythagorean triangles in which the sum of the area and the shortest leg is a square.   Here are the first three examples:                             … Continue reading

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Pythagorean triangle whose perimeter is p^2 and area p^3

    Find a Pythagorean triangle whose perimeter is a square     such that     equals the area. Here are two examples:       Any other example?                     … Continue reading

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Triangular numbers between consecutive square numbers

    Let     be the n-th m-gonal number,   m-gonal number with index     ……….       Checking up to 50 the following proposition: If there are exactly two triangular numbers between     and   … Continue reading

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A^n + B^n + C^n = D^n + E^n + F^n, n = 2,6

                                                       

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SquareFree semiprimes n, σ(n), φ(n), and σ(n) * φ(n)

      is the sum of divisors function Euler’s totient function   is the number of positive integers not exceeding     that have no common divisors with     (other than the common divisor 1). In other words, … Continue reading

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Identity of two equal sums of n distinct squares

    Establish the following identity:                                          

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Oblong numbers : x(x+ 1), y(y+ 1), z(z+ 1) in arithmetic progression

  An Oblong number is a number which is the product of two consecutive integers, that is, a number of the form       There exist infinitely many triplets of positive integers   ,   for which the numbers … Continue reading

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Fibonacci in arithmetic progression

    Fibonacci numbers is defined by the recurrence relation: then,   giving us all increasing arithmetic progressions formed of three terms of the Fibonacci sequence For example,     Prove that there are no increasing arithmetic progressions formed of … Continue reading

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