Integers

[huneynumb]

Express 1991 as a sum of consecutive positive integers and show that this is the only way to do it.

[GutZ]

Like A+B+C+D = 1991?

 

How many numbers can we use?

[Severian]

1991 = 994 +995 but I am not sure how to prove that it is the only case (induction maybe)

[Tartaglia]

Don't the 22 consecutive numbers 80,81,82...101 add up to 1991?

[Tartaglia]

What about the 11 consecutive integers 176,177, 178,...186?

[Bignose]

1991 = 994 +995 but I am not sure how to prove that it is the only case (induction maybe)

 

1991=996 + 995

[Tartaglia]

The proof or otherwise of this problem revolves around the factors of 1991

 

Since for an arithmetic progression S(n) = (n/2)*(2a+(n-1)d) either n/2 or n must be a factor of 1991. This means the string of digits can only be 1,11,181 long or 2,22,362.