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Power Quady

Find all real solutions of the equation (x^2-7x+11)^(x^2-11x+30) = 1.

Telescoping Series

Find $S_r = 1^r + 2^r + 3^r + ... + n^r$ where r is any fixed positive integer in terms of $S_1, S_2, ... S_{r-1}$.


Which is larger: (a) 1.000001^{1000000} or 2? (b) 100^{300} or 300! (i.e.factorial 300)


Age 16 to 18 Challenge Level:

This problem was suggested by Yatir Halevi.

Solve the equation:


Solve the equation:


Can you find solutions to all equations of the form:


where the sequence of powers is defined in the same way and $a$ is a positive integer?

Explain what you have done and prove that you have found all possible solutions.