Unverified50% confidenceFactExact time
The repunit sequence R₁=1, R₂=11, R₃=111... produces remainders modulo an integer N that fall within only N possible values from 0 to N-1; examining the first N+1 terms guarantees two remainders are equal, and their difference is divisible by N.
1
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50%
Confidence
Long-term
Relevance
9/27/2026
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Related Claims
UnverifiedThe repunit Rₙ = (10ⁿ - 1)/9 itself contains no factor of 2 or 5, because 10ⁿ - 1 always ends in 9, meaning it is odd and not divisible by 5.73% similarUnverifiedThe weakened proposition asks: can any even number greater than 2 necessarily be written as the sum of two numbers whose Liouville value is -1?67% similarUnverifiedThe R² coefficient of determination ranges between 0 and 1, calculated by the formula R² = 1 - RSS/TSS, and represents the proportion of the total variance in the dependent variable explained by the model.65% similarUnverifiedAdding 7 and then taking modulo 7 is equivalent to doing nothing, and can be used to shift negative remainders into the positive range.65% similarUnverifiedThe smallest n for which 10ⁿ ≡ 1 (mod N) holds is called the multiplicative order of 10 modulo N, and it determines the number of digits in the final answer.64% similar
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