Solve for this number with repeated digits.
Let be the smallest positive integer such that is a number all whose digits are equal. What is ?
Pre-Indian Regional Mathematical Olympiad -- 2019
The answer is 12345679.
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1 solution
LHS = 45N = 9 * 5 * N. RHS has to be a number with repeated digits and as N is divisible by 5 , the RHS has to be a number containing 5 or 0.
Therefore RHS is a number with repeated 5s. Since LHS is also divisible by 9 the smallest length of RHS is 9 digits containing all 5s in all the placeholders.
So RHS = 555555555, N = 555555555/45 = 12345679