Tag Archives: Concatenation

Concatenation : a || b = n^2 + a = (n+1)^2 – b

    Notice that The integer N = 122 can be partitioned into two parts, 1 and 22, so that the first part is the difference between N and the greatest square less than N, and the second part is … Continue reading

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Concatenation: aa||bb||cc||dd + 1, aaa||bbb + 1 are squares

    Numbers of the form     such that     is a square :     …………………….. …………………….. …………………………. …………………………. ………………………. ……………………….   Numbers of the form     is a square : ……………………………. …………………………….     ………………………………… … Continue reading

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Concatenations : x || y || z = (x + y + z)^3

                                    For example,     Can you find other solutions?                                          

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Concatenation | 7-digit number abc = a || b || c

    a,   b,   c   are in arithmetic progression a   ||   b   ||   c   =   abc   is a 7-digit number Find the largest 7-digit number obtained in this way.   … Continue reading

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Concatenations : x || y = x^2/2 + 2*y^2

    where     and     are positive integers                                                  

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Concatenation: 2^n || 2^(n+1)

    Let     be any positive integer.   Prove that     is always a multiple of 3.                                  

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Concatenations: x^2 || 2^2 = y^2

                                               

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Concatenations x^2 || 3^2 = y^2

  Here are the first few solutions to                                                                               

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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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When the Concatenation of n || (n+1) is Octagonal

    Octagonal numbers are of the form      We can write Or the integer length of     is     Here are the first few solutions   n   =   1,   2,   5,   … Continue reading

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