Monthly Archives: November 2016

3 x 3 magic square w/ entries are distinct integer squares

             …..     …..            …..     …..            …..     …..   is a magic square,   Can you find a number     such that                                ——————————————–              … Continue reading

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Integer n such that 2*n^2 can be written as sum of two squares in four ways

    Find the least integer     such that     can be written as sum of two squares in four ways   Also, find the next few ones.     Find the least integer     such that … Continue reading

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4X4 grid – gcd from 1 to 24

    To place distinct integers in a   n × n   grid such that all gcds from   1   to   2*n(n-1)   are generated.   If   n = 4,   then find 16 integers such … Continue reading

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3X3 grid – gcd from 1 to 12

    To place distinct integers in a n × n grid such that all gcds from 1 to 2*n(n-1) are generated.   If   n = 3,   then find 9 integers such that all gcds from   1 … Continue reading

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Integers (a,b,c,d); each pairwise sum & sum of all four is a square

    Find four integers     such that   are all squares   The first few solutions are: Also found by pipo                                   … Continue reading

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Pythagorean triangle {a+b+c, a^2+b+c, a+(b+c)^2} are to made squares

    Find a Pythagorean triangle     such that     are all squares                                                   … Continue reading

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Marrakech climate summit COP22 — Palindromic numbers

                                                   

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Diophantine equation : y^2 – p = 2^n, where p is a prime number

    The diophantine equation     where     is a prime number   < 100   The only solutions to the diophantine equation     with   y > 0   are given by     (n, y)   =   … Continue reading

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Diophantine equation : 2^a + 2^b + 2^c = x^2

    Consider the Diophantine equation : for     nonnegative integers,                                                      

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Diophantine equation : (a-b)/(a+b) + (b-c)/(b+c) + (c-d)/(c+d) + (d-a)/(d+a) = 0

    Determine integral solutions of the Diophantine equation     where     are distinct   Solutions: ,     ,     If   ,   then     ,     If   ,   then     ,         … Continue reading

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