# 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

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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

## 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

………………………… ………………………… …………………………

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

Explain this   …………………. ………………….

## 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)