Monthly Archives: March 2015

Triangular Num3ers| T(n)^4 = ((1^5 + 2^5 + … + n^5) + (1^7 + 2^7 + … + n^7))/2

    …………………….. ……………………..       Prove for all n positive integers that                             Advertisements

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Num3er 315

  315   has 12 divisors:    1    3    5    7    9    15    21    35    45    63    105    315 Sum of divisors:    624             … Continue reading

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Is the Triangular number T(11…11) (2n ones) always a palindromic number?

        Is the triangular number     (2n ones) always a palindromic number?                                            

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Triangular number| n^3 = T(n)^2 – (T(n) – n)^2

        ………………………… ………………………… …………………………                                      

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Why is every 4-th power > 1 the sum of two triangular numbers?

  Explain this   …………………. ………………….                                        

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System of equations: x^(x+y) = y^12 and y^(x+y) = x^3

      Hint:   the solutions are:          Solve analytically                        

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Equation| x^x = (x-y)^(x+y)

    x and y are positive integers. Is there a solution to   Paul found:   ……….                            

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x^(y^z) = y^(z^x) = z^(x^y)

                               

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Num3er 144 – Remarkable Property

    Each of its first 50 multiples differs from the first perfect square (S) by a perfect square, for the exceptions of     The pattern breaks here:   Find another example… …then show that, for any positive integer … Continue reading

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Sets of 3 triangular numbers in geometric progression

    In a geometric progression, any three consecutive terms   a,   b   and   c will satisfy the following equation:     common ratio = 6,     ,      ,      ,      common ratio = 35/6 … Continue reading

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