Type Ńdẹ́bẹ́ ↗

Arithmetic in Ńdẹ́bẹ́ Numerals

Divisibility Tests

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11. Vigesimal Divisibility Tests

These allow a reader to check divisibility without dividing. They are base-20-internal: only the number's own digits are examined.

Divisor Test Type
2 Units digit is even (0, 2, 4, 6, 8, 10, 12, 14, 16, 18) — its body is 0B, 2B or 4B with an even flag level, or 1B/3B with an odd one Last-digit test
3 Alternating digit sum is divisible by 3 Alternating-sum test
4 Units digit is one of {0, 4, 8, 12, 16} Last-digit test
5 Units digit is 0, 5, 10, or 15 — its body contribution is zero (0B) Last-digit test
6 Divisible by both 2 and 3 Composite
7 Alternating digit sum is divisible by 7 Alternating-sum test
10 Units digit is 0 or 10 Last-digit test
11 From right to left, multiply digits by repeating weights 1, −2, 4, 3, 5, 1, … and add. The sum must be divisible by 11. Weighted-sum test
19 Digital root (repeated digit sum) is divisible by 19 Digit-sum test
 20 Units digit is 0 Last-digit test
− + =
For 3 and 7: 441 is [1, 2, 1] in base 20; 1 − 2 + 1 = 0, so it is divisible by both. For 11, use the weighted rule: 22 is [1, 2], and 2 − 2 × 1 = 0.

Notes: - The ÷5 test is visually immediate in Ńdẹ́bẹ́: look at the units glyph — a zero-valued body means divisible by 5. The complete numerals 5, 10, and 15 retain their plain bodies; do not replace them with isolated flags. - The alternating-sum tests for 3 and 7 work because 3 × 7 = 21 = one more than the base (as 11 in base 10). - The digital-root test for 19 works because 19 = one less than the base (as 9 in base 10).

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