06-25-2017, 04:38 AM
(This post was last modified: 06-25-2017, 02:29 PM by Dane Regan.)
Voted
The only two digit square number that can be expressed as the sum of 5 consecutive integers
[spoiler]25
Reasoning:
Every number that is the sum of 5 consecutive integers must be a multiple of 5 as
n + (n+1) + (n+2) + (n+3) + (n+4) = 5n + 10 = 5(n + 2)
So, the smallest square number that has this property must be 25 (5^2).
The second smallest is consequently 100 = 2^2 * 5^2 = 10^2, which has 3 digits.[/spoiler]
The only two digit square number that can be expressed as the sum of 5 consecutive integers
[spoiler]25
Reasoning:
Every number that is the sum of 5 consecutive integers must be a multiple of 5 as
n + (n+1) + (n+2) + (n+3) + (n+4) = 5n + 10 = 5(n + 2)
So, the smallest square number that has this property must be 25 (5^2).
The second smallest is consequently 100 = 2^2 * 5^2 = 10^2, which has 3 digits.[/spoiler]