Saturday, 11 February 2017

(√3+√2)^(2n)

A nice mathematics problem found on the University of Waterloo's CEMC (Centre for Education in Mathematics and Computing) website:

For each positive integer n, define an and bn to be the positive integers such that (3 2)2n an bn6 and (3  2)2n an − bn6.

(a)  Determine the values of aand b2.

(b)  Prove that 2an − (3 + 2)2n 2an for all positive integers n.

(c)  Let dn be the units digit of the number (3 2)2n when it is written in decimal form. Determine, with justification, the value of ddd+  ... + d1865 d1866 d1867.

The solution can be found here (Part B #3) if you want to check it out.

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