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

Revision as of 00:18, 20 May 2017

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.

@@ Line 1: / Line 1: @@
 == Problem ==
+ Powerless Progressions
+Find an infinite sequence of integers <math>a_1, a_2, a_3, \ldots</math>  that has all of
+these properties:
+(1) <math>a_n = c + dn</math> with c and d the same for all <math>n = 1, 2, 3, \ldots</math>
+(2) <math>c</math> and <math>d</math> are positive integers, and
+(3) no number in the sequence is the <math>r^{th}</math> power of any integer, for any power <math>r = 2, 3, 4, \ldots</math>
+Reminder: Justify answers. In particular, for maximum credit, make it clear in your presentation
+that your sequence possesses the third property.
 == Solution ==

2017 UNCO Math Contest II (Problems • Answer Key • Resources)
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