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**nazz** The sum of first N integers is a three digit number with all of its digits equal, what is the value of N?

1,2,3,4,5,6,7……………. Is an arithmetic series

S= n/2[2a + (n-1) d] = n (n +1) / 2

n (n +1) / 2 = 111x

Since sum of first integers is a three digit number with all digits equal

Hence it xxx = 100x +10x +x = 111x.

By trial and taking x=6, and solving for n, n2 +n – 1332 = 0, I will get n=36, is there any other way of solving;

n (n +1) / 2 = mod 111, and getting value of n=36 from this equation?