 Art. 445 that a number is divisible by 11 when the difference between the sum of the digits in the odd places and the sum of the digits in the even places is divisible by 11.  Arithmetic - Σελίδα 27των A G. Blake - 1885Πλήρης προβολή - Σχετικά με αυτό το βιβλίο
 | James Wood - 1845 - 442 σελίδες
...number be divisible by r—l, the number itself is divisible by r-1. Similarly, it may be shewn that, if the difference between the sum of the digits in the...places and the sum of the digits in the even places be divisible by r+ 1, the number is divisible by r + 1. Рвов. Toßnd what numbers are divisible... | |
 | Isaac Todhunter - 1858 - 530 σελίδες
...notation of which the radix is r, any whole number when divided by r + l will leave the same remainder as the difference between the sum of the digits in the...places and the sum of the digits in the even places leaves when divided by r + 1. With the same notation as in the preceding proposition we have + ......... | |
 | Isaac Todhunter - 1860 - 620 σελίδες
...which tJie radix is r, any wJiole number when divided by r + 1 will leave the same remainder as tlte difference between the sum of the digits in the odd places and the ev/m of the digits in the even places leaves when divided by r + 1. With the same notation as in the... | |
 | Edward Brooks - 1863 - 350 σελίδες
...number is then a number of tens, which is divisible by 10. PROP. X. — Every number is divisible by 11 when the difference between the sum of the digits in the odd places and even places it divisible by 11. DEM. — This may be proven by trial and induction. Thus,* take 7853648... | |
 | Woolwich roy. military acad - 1864 - 588 σελίδες
...the radix is (r) show that any whole number when divided by (r + l) will leave the same remainder as the difference between the sum of the digits in the...places and the sum of the digits in the even places leaves, when divided by (r+1). Express 240'25 in the scale whose radix is (8) and extract the square... | |
 | Isaac Todhunter - 1866 - 618 σελίδες
...444. In a scale of notation in which the radix is r let any whole number be divided by r + 1 ; and let the difference between the sum of the digits in the...places and. the sum of the digits in the even places be divided by r + l ; then either the remainders will be equal or their sum will be r+l. With the same... | |
 | Isaac Todhunter - 1866 - 580 σελίδες
...digits of that number were divided by 9. It appears from Art. 444 that a number is divisible by 11 when the difference between the sum of the digits in the odd ..J places and the sum of the digits in the even places is divisible by 11. 447. From the property... | |
 | William Harding Girdlestone - 1867 - 368 σελίδες
...8. 9, when the sum of their digits is divisible by 9. 10, when they have 0 in the units' place. 11, when the difference between the sum of the digits...the sum of the digits in the even places is either 0, or is divisible by 11. 12, when the two right-hand digits are divisible by 4, and the sum of the... | |
 | Samuel H. Winter - 1867 - 468 σελίδες
...which the radix is r, show that any whole number when divided by rf 1 will leave the same remainder as the difference between the sum of the digits in the...places and the sum of the digits in the even places, when divided by r+1. R (2) Express 240-25 in the scale whose radix b 8, and extract the square root... | |
 | William Harding Girdlestone - 1870 - 482 σελίδες
...8. 9, when the sum of their digits is divisible by 9. 10, when they have 0 in the units' place. 11, when the difference between the sum of the digits...places and the sum of the digits in the even places is cither 0, or is divisible by 11. 12, when the two right-hand digits are divisible by 4, and the sum... | |
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