Sums of consecutive numbers

Find the largest three-digit number that can be written as a sum of two or more positive consecutive integers exactly in three different ways.


The answer is 996.

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3 solutions

996 has two odd divisors the answer will be 969 = 3 * 17 * 19

Kushal Bose - 2 years, 6 months ago

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996 has three odd divisors, 3,83,249. 969 has 3,17,19,51,57,323,969. Those are 7 odd divisors.

A Former Brilliant Member - 2 years, 6 months ago

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So it can be expressed more than 3 ways ?

Kushal Bose - 2 years, 6 months ago

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@Kushal Bose 969 can be expressed as a sum in seven different ways.

A Former Brilliant Member - 2 years, 6 months ago
Vinod Kumar
May 10, 2020

Solve (n+1)(2m+n)/2=996 gave 996 as maximum with following three solution:

m=30, n=23

m=121, n=7

m=331, n=2

996 is the sum of the ranges of 30 to 53, 121 to 128 and 331 to 333, each range inclusive.

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