SOLUTION: In how many ways can the number 105 be written as the sum of two or more consecutive positive integers?

Question 1204310: In how many ways can the number 105 be written as the sum of two or more consecutive positive integers?

Found 2 solutions by MathLover1, ikleyn:
Answer by MathLover1(20850) (Show Source): You can put this solution on YOUR website!
You want and such that
+.....+
=+(+.....+)
=,

which is equivalent to
.
Notice that, obviously, , therefore , whence , so
∈{ ,,,,,, }...(i.e. all the divisors of that are ≤- a total of cases).

here they are:

1. If then ; it follows that and , so you have
.2 If then ; it follows that and , so you have
.
3. If then 2; it follows that and, so you have
.
4. If then ; it follows that and , so you have
.
5 If then ; it follows that and , so you have

.
6. If then ; it follows that and, so you have
.
7. If then ; it follows that and , so you have
.

Answer by ikleyn(52794) (Show Source): You can put this solution on YOUR website!
.

The "solution" in the post by @MathLover 1 is one-to-one copy-paste from this web-page

https://math.stackexchange.com/questions/2088608/sum-as-an-increasing-sequence-of-two-or-more-consecutive-integers

without any reference, naturally.

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