Difference between revisions of "2017 UNCO Math Contest II Problems/Problem 10"

(Problem)
(Solution)
Line 16: Line 16:
  
 
== Solution ==
 
== Solution ==
 +
2, 6, 10, 14… (& other possibilities)
  
 
== See also ==
 
== See also ==

Revision as of 03:12, 13 January 2019

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

2, 6, 10, 14… (& other possibilities)

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