Mathematical Proofs
This page contains some formal mathematical proofs referred to elsewhere on this site. All in PDF form.
- Every composite number has a prime divisor not greater than its square root.
- A number is divisible by 3 if and only if the sum of its digits is divisible by 3.
- A number is divisible by 7 if the number formed by removing the last digit and subtracting two times that digit from the remaining number is also divisible by 7.
- A three-digit number is divisible by 11 if the sum of the outer two digits equals the value of the inner digit (modulo 11).
- A number is divisible by 13 if the number formed by removing the last digit and adding four times that digit to the remaining number is also divisible by 13.
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This page first published 15 July 2026. Last updated 15 July 2026
