...Therefore, etc. 2. A number is exactly divisible by 9 when the sum of its digits is divisible by 9. 3. The difference between any number and the sum of its digits is divisible by 9. 4. A number divided by 9 will leave the same remainder if the order of the figures is changed. 5....

...other; (d) that any number which is divisible by two other numbers will be divisible by their L. c. M. ; (e) that one-third of the difference between...divisible by 3 ; (/) that every prime number but 2 can bo made composite by tho addition or subtraction of unity ; (¡7) that every prime number greater than...

...... an be in harmonical progression, then "+03+ • • +«„ are also in harmonical progression. 7. The difference between any number and the sum of its digits is divisible by r — I, where r is the radix of the scale in which the number is expressed. In the scale whose radix...

...3x9 + 5; therefore 875426 divided by 9 also gives remainder 5. In the same way it can be shown that the difference between any number and the sum of its digits, is always divisible by 9. *61. Similarly it may be shown that a number is divisible by 3 when the sum...

...decimal system the difference between any number and the sum of its digits is divisible by 9. 538. Since the difference between any number and the sum of its digits is a multiple of r — l, r being the radix, and since the number that must be added to this multiple...

...ABCD will be a maximum when AB = §a, and that this maximum volume is -A- a8. LXXXIV. 1. Prove that the difference between any number and the sum of its digits is divisible by 9, and that the quotient is the sum of the numbers which remain when the digits of the original number...