Fix repunit divisibility edge case for prime 3

Author: nickzerjeski

Maths/RepunitTheorem.js

@@ -4,7 +4,7 @@
  * A repunit of length n is:
  *   R_n = (10^n - 1) / 9
  *
- * For a prime p (p != 2, 5), p divides R_n iff ord_p(10) divides n.
+ * For a prime p (p != 2, 3, 5), p divides R_n iff ord_p(10) divides n.
  * Reference: https://en.wikipedia.org/wiki/Repunit
  */
 
@@ -69,6 +69,7 @@ const isRepunitDivisibleByPrime = (length, prime) => {
 
   const p = BigInt(prime)
   if (p === 2n || p === 5n) return false
+  if (p === 3n) return BigInt(length) % 3n === 0n
   if (gcd(10n, p) !== 1n) return false
 
   const order = multiplicativeOrder10(p)

Maths/test/RepunitTheorem.test.js

@@ -21,6 +21,8 @@ describe('RepunitTheorem', () => {
   })
 
   it('returns false when divisibility condition does not hold', () => {
+    expect(isRepunitDivisibleByPrime(1, 3n)).toBe(false)
+    expect(isRepunitDivisibleByPrime(3, 3n)).toBe(true)
     expect(isRepunitDivisibleByPrime(6, 19n)).toBe(false)
     expect(isRepunitDivisibleByPrime(9, 2n)).toBe(false)
     expect(isRepunitDivisibleByPrime(9, 5n)).toBe(false)