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Omni-MATH / Suppose that a positive integer N can be expressed as the sum of k consecutive positive integers N=a+(a+1)+(a+2)+⋯+(a+k−1) for k=2017 but for no other values of k>1. Considering al…

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problem

Suppose that a positive integer NN can be expressed as the sum of kk consecutive positive integers N=a+(a+1)+(a+2)+⋯+(a+k−1) N = a + (a+1) +(a+2) + \cdots + (a+k-1) for k=2017k=2017 but for no other values of k>1k>1. Considering all positive integers NN with this property, what is the smallest positive integer aa that occurs in any of these expressions?
Plain-text mathematical notation (without MathML)
Suppose that a positive integer N can be expressed as the sum of k consecutive positive integers N=a+(a+1)+(a+2)+⋯+(a+k−1) for k=2017 but for no other values of k>1. Considering all positive integers N with this property, what is the smallest positive integer a that occurs in any of these expressions?
Original LaTeX notation
Suppose that a positive integer $N$ can be expressed as the sum of $k$ consecutive positive integers \[ N = a + (a+1) +(a+2) + \cdots + (a+k-1) \] for $k=2017$ but for no other values of $k>1$. Considering all positive integers $N$ with this property, what is the smallest positive integer $a$ that occurs in any of these expressions?

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Source and history

task_id
6119fa35-3149-5b6e-b8f4-4058fce50906
task_key
test--6119fa35-3149-5b6e-b8f4-4058fce50906
task_revision_id
1
config / split
/ test

Official source

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