
PreCalculus PreCalculus Math Forum 
 LinkBack  Thread Tools  Display Modes 
September 8th, 2018, 09:46 AM  #1 
Newbie Joined: Sep 2018 From: US Posts: 1 Thanks: 0  Sum of a nondecreasing sequence of integers
For which pairs of positive integers $(n, d)$ is it true that every integer $S$ can be written as a sum of a nondecreasing sequence of integers $a_1+a_2+...+a_n$ and $a_na_1=d$?

September 8th, 2018, 04:09 PM  #2 
Math Team Joined: Oct 2011 From: Ottawa Ontario, Canada Posts: 13,804 Thanks: 971 
That's sure confusing, Jimbo. Are you talking about an arithmetic sequence? Say sequence is 1,2,3 a1=1, a2=2, an = 3 (n = 3) 1 + 2 + 3 = 6 = S ? (n,d) = 3,2)? What does "every integer S" mean? Any integer? 
September 8th, 2018, 06:56 PM  #3 
Math Team Joined: Dec 2013 From: Colombia Posts: 7,566 Thanks: 2567 Math Focus: Mainly analysis and algebra 
I have a vague feeling that there may be no such pairs. I have a stronger feeling that I'm probably wrong about that. 
September 8th, 2018, 07:06 PM  #4 
Math Team Joined: Oct 2011 From: Ottawa Ontario, Canada Posts: 13,804 Thanks: 971  
September 8th, 2018, 08:09 PM  #5 
Math Team Joined: Dec 2013 From: Colombia Posts: 7,566 Thanks: 2567 Math Focus: Mainly analysis and algebra 
Nothing stronger than tea tonight. (Sorry Jonah, you can have mine).


Tags 
integers, nondecreasing, sequence, sum 
Thread Tools  
Display Modes  

Similar Threads  
Thread  Thread Starter  Forum  Replies  Last Post 
Prove that X contains a strictly decreasing sequence?  NeoXx  Real Analysis  3  November 23rd, 2015 03:39 PM 
sequence increasing or decreasing  aaronmath  Calculus  4  November 6th, 2011 10:26 AM 
Sequence of integers  proglote  Number Theory  5  October 19th, 2011 11:37 AM 
Sequence of integers  proglote  Number Theory  4  October 11th, 2011 08:11 AM 
Sequence (eventually) increasing or decreasing or neither  everettjsj2  Calculus  2  February 25th, 2010 09:26 PM 