2017 UNCO Math Contest II Problems/Problem 10

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Problem

Powerless Progressions 

Find an infinite sequence of integers $a_1, a_2, a_3, \ldots$ that has all of these properties:

(1) $a_n = c + dn$ with c and d the same for all $n = 1, 2, 3, \ldots$

(2) $c$ and $d$ are positive integers, and

(3) no number in the sequence is the $r^{th}$ power of any integer, for any power $r = 2, 3, 4, \ldots$

Reminder: Justify answers. In particular, for maximum credit, make it clear in your presentation that your sequence possesses the third property.

Solution

See also

2017 UNCO Math Contest II (ProblemsAnswer KeyResources)
Preceded by
Problem 9
Followed by
Problem 11
1 2 3 4 5 6 7 8 9 10
All UNCO Math Contest Problems and Solutions