Tag Archives: Oblong number

Triangular oblongs : a(a+1) = b(b+1)/2

    An Oblong number is a number which is the product of two consecutive integers, that is, a number of the form   A Triangular number is a number of the form   A Triangular oblong number:     … Continue reading

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Palindromic Oblong numbers for palidromic/non-palidromic indices

    Oblong number is palindromic for any palidromic index of the form ,   where   ,   ,   ,   ,   ,   ,       and for non-palindromic index of the form ,   … Continue reading

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Oblong numbers| primes solutions of p(p+1) + q(q+1) = r(r+1)

    An Oblong number is a number which is the product of two consecutive integers, that is, a number of the form       Find primes solutions     of the equation                Prove that the solution … Continue reading

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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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Prime numbers 127, 3697, 5227

      are prime numbers such that the numbers ,    ,    form an arithmetic progression :   Find other such numbers     The problem may be expressed as follows: find three triangular numbers with prime indices, … Continue reading

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Oblong numbers | O(a) + O(b) = O(c) – O(d)

    An Oblong number is a number which is the product of two consecutive integers, that is, a number of the form   Let     be the n-th oblong number, for   Show that there are infinitely many … Continue reading

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Concatenations Oblong numbers| O(n) || x^2 = A^2

    An Oblong number is a number of the form     Here are the first few solutions for                                           … Continue reading

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Squares & Oblong numbers| 1*2 – 2*3 + 3*4 – 4*5 + … + (-1)^(n-1) n(n+1)

    An Oblong number is a number of the form       Let     Determine the values of     for which (1)     is a square number (2)     is an Oblong number   … Continue reading

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Difference between an Oblong number and Pentagonal is 1

  Oblong numbers are of the form ,     where     is the n-th triangular number.   An integer of the form     is called a Pentagonal number.   The first few solutions are :       … Continue reading

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