| Tom M. Apostol - Mathematics - 1998 - 340 pages
...two examples to illustrate their usefulness. EXAMPLE 1 Test for divisibility by 9. An integer n > 0 **is divisible by 9 if, and only if, the sum of its digits in** its decimal expansion is divisible by 9. This property is easily proved using congruences. If the digits... | |
| Serge Lang - Mathematics - 2001 - 371 pages
...integer is divisible by 3 if and only if the sum of its digits is divisible by 3. (b) Prove that it **is divisible by 9 if and only if the sum of its digits** is divisible by 9. (c) Prove that it is divisible by 1 1 if and only if the alternating sum of its... | |
| Neal Koblitz - Mathematics - 1994 - 235 pages
...decimal integer is divisible by 3 if and only if the sum of its digits is divisible by 3, and that it **is divisible by 9 if and only if the sum of its digits** is divisible by 9. 5. Prove that n 5 — n is always divisible by 30. 6. Suppose that in tiling a floor... | |
| Neal Koblitz - Mathematics - 1994 - 235 pages
...decimal integer is divisible by 3 if and only if the sum of its digits is divisible by 3, and that it **is divisible by 9 if and only if the sum of its digits** is divisible by 9. 5. Prove that n 5 — n is always divisible by 30. 6. Suppose that in tiling a floor... | |
| Ravi Vakil - Mathematics - 1996 - 254 pages
...Thus M is divisible by 2 if and only if its last digit is divisible by 2! Divisibility by 9 i A number **is divisible by 9 if and only if the sum of its digits** is divisible by 9. (This method can easily be repeated. For example, to test if 1234567890 is divisible... | |
| Bharath Sethuraman - Mathematics - 1996 - 192 pages
...99, and 999 as far as divisibility by 3 is concerned? Then, what does Lemma 1 .2 suggest?) (e) Prove **that an integer is divisible by 9 if and only if the sum of its digits** is divisible by 9. (0 Prove that an integer is divisible by 11 if and only if the difference between... | |
| Steven George Krantz - Mathematics - 1997 - 465 pages
...explain the reason in the following way: Notice that 45 is divisible by 9. We know that any number **is divisible by 9 if and only if the sum of its digits** is divisible by 9. In fact, any positive integer, divided by 9, has the same remainder as the remainder... | |
| Peter J. Eccles - Mathematics - 1997 - 350 pages
...positive integer is written in decimal notation as n = Ofcofc-i... O2oiOO where 0 ^ <ц < 9. Prove that n **is divisible by 9 if and only if the sum of its digits** Ofc + uk-i + ... + G1 + Û0 is divisible by 9. 4. Suppose that a positive integer is written in decimal... | |
| Wade Sherard - Education - 1998 - 128 pages
...digits is 34, which yields 7 after casting out 9's And, 9 7=2, the missing digit. Property 4: A number **is divisible by 9 if and only if the sum of its digits** is divisible by 9 Let N be the serial number and let S be the “scrambled” number Suppose that N... | |
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