Repunits and Repetends

algebraic divisors base companion loop composite number concatenation congruent conjecture Corollary cyclic permutations cyclotomic polynomial D. H. Lehmer decimal representation digit sum divisors of repunits example Factor Principle fraction whose denominator full period prime H. C. Williams Harshad Harshad number integer k-power residue known prime large number least common multiple least one primitive length of prime less Mersenne primes Midy property number of digits number of primes number system number theory odd number odd period lengths pair palindrome period length equal positive integer primality prime factors prime number Prime Period Lengths prime repunits primes in Set primitive cofactor primitive prime divisors primitive root primitive solution Proof proper divisor proper fractions pseudoprime quadratic residue quotient R₁ reduced fraction relatively prime repdigit repetend representative numbers repunits whose subscripts residue index rightmost smallest repunit divisible square sum multiples Table tion unity loop YG(n