My Math Forum Sum of a non-decreasing sequence of integers

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 September 8th, 2018, 08:46 AM #1 Newbie   Joined: Sep 2018 From: US Posts: 1 Thanks: 0 Sum of a non-decreasing 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 non-decreasing sequence of integers $a_1+a_2+...+a_n$ and $a_n-a_1=d$?
 September 8th, 2018, 03:09 PM #2 Math Team   Joined: Oct 2011 From: Ottawa Ontario, Canada Posts: 14,597 Thanks: 1038 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, 05:56 PM #3 Math Team   Joined: Dec 2013 From: Colombia Posts: 7,674 Thanks: 2654 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, 06:06 PM   #4
Math Team

Joined: Oct 2011

Posts: 14,597
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Quote:
 Originally Posted by v8archie I have a vague feeling that there may be no such pairs. I have a stronger feeling that I'm probably wrong about that.
I have a still stronger feeling that you're drunk

 September 8th, 2018, 07:09 PM #5 Math Team   Joined: Dec 2013 From: Colombia Posts: 7,674 Thanks: 2654 Math Focus: Mainly analysis and algebra Nothing stronger than tea tonight. (Sorry Jonah, you can have mine).

 Tags integers, nondecreasing, sequence, sum

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