 | George Baron - 1804 - 318 σελίδες
...digits, a-\-b+c, there remains axr* — \+bxr— . l=(axr+l +6)'xr— I=(ax'-+l+i)x9: since, therefore, the difference between any number and the sum of its digits is divisible by 9, it evidently follows that the number and the sum of its digits, divided by 9, leave either none... | |
 | James Maginness - 1821 - 378 σελίδες
...its digits,n+&+c there remains axr2— 1+frxr— I=(axr+l-f6) xr^I = (axr+l+6)x9: Since, therefore, the difference between any number and the sum of its digits is divisible by 9, or 3, it evidently follows, that the number and sum of its digits, divided by 6, or 3, leave either... | |
 | George Roberts Perkins - 1849 - 356 σελίδες
...9, will give the same remainder as will be found by dividing the sum of its digits by 9, therefore the difference between any number and the sum of its digits is exactly divisible by 9. From the above property, a very interesting arithmetical puzzle is deduced.... | |
 | George Roberts Perkins - 1850 - 356 σελίδες
...9, will give the same remainder as will be found by dividing the sum of its digits by 9, therefore the difference between any number and the sum of its digits is exactly divisible by 9. From the above property, a very interesting arithmetical puzzle is deduced.... | |
 | John Groesbeck - 1867 - 226 σελίδες
...number divided by 3 or 9 will leave the same remainder as the sum of its digits divided by 3 or 9. The difference between any number and the sum of its digits is a multiple of 9. The difference between a number and the digits of the same number arranged in another... | |
 | John Groesbeck - 1868 - 350 σελίδες
...number divided by 3 or 9 will leave the same remainder as» the sum of its digits divided by 3 or 9. The difference between any number and the sum of its digits is a multiple of 9. The difference between a number and the digits of the same number arranged in another... | |
 | John Groesbeck - 1871 - 370 σελίδες
...number divided by 3 or 9 will leave the same remainder as the sum of its digits divided by 3 or 9. The difference between any number and the sum of its digits is a multiple of 9. The difference between a number and the digits of the same number arranged in another... | |
 | John Groesbeck - 1875 - 378 σελίδες
...number divided by 3 or 9 will leave the same remainder as tie sum of its digits divided by 3 or 9. The difference between any number and the sum of its digits is a multiple of 9. The difference between a number and the digits of the same number arranged in another... | |
 | Edward Brooks - 1876 - 588 σελίδες
...readily inferred: 2. A number is exactly divisible by 9 wlien the sum of Us 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 gives the same remainder as any one formed by changing the order of the... | |
 | Adolf Sonnenschein - 1877 - 98 σελίδες
...other ; (d) that any number which is divisible by two other numbers will be divisible by their LCM ; (e) that one-third of the difference between any number...composite by the addition or subtraction of unity ; (g) that every prime number greater than 3 can be made a multiple of 6 either by the addition or... | |
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Any number divided by 3 or 9 will leave the same remainder as the sum of its digits divided by 3 or 9. The difference between any number and the sum of its digits is a multiple of 9. The difference between a number and the digits of the same number arranged... 
