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" A number is divisible by 11 if the difference between the sum of the digits in the even places and the sum of the digits in the odd places is either 0 or a multiple of 11. "
Elementary Algebra - Page 328
by James Hamblin Smith - 1870
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The elements of algebra

James Wood - Algebra - 1845 - 442 pages
...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 odd 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...
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Algebra

Isaac Todhunter - Algebra - 1858 - 528 pages
...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 odd 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...
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Algebra

Isaac Todhunter - 1860 - 622 pages
...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...
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A Compendium of facts and formulæ in pure mathematics and natural philosophy

G. R. Smalley - Mathematics - 1862 - 190 pages
...respectively. IV. Every number is divisible by 11 when the difference between the sum of the figures in the odd places and the sum of those in the even places is divisible by 11. V. Every compound number will divide a given quantity when its component factors...
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The Normal Written Arithmetic: By Analysis and Synthesis, Designed for ...

Edward Brooks - Arithmetic - 1863 - 350 pages
...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...
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Report on the examination for admission to the Royal military academy at ...

Woolwich roy. military acad - 1864 - 588 pages
...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 odd 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...
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Algebra for the Use of Colleges and Schools: With Numerous Examples

Isaac Todhunter - Algebra - 1866 - 614 pages
...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 odd 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...
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Artithmetic theoretical and practical

William Harding Girdlestone - 1867 - 368 pages
...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 in the odd places and the sum of the digits in the even places is either 0, or is divisible by 11. 12, when the two right-hand digits...
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Mathematical Exercises ...

Samuel H. Winter - 1867 - 472 pages
...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 odd 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...
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The Teacher's Manual: Containig a Treatise Upon the Discipline of the School ...

Hiram Orcutt - School discipline - 1871 - 288 pages
...some multiple of 11. Explanation. Every number is composed of a certain number of ll's plus or minus the difference between the sum of the digits in the odd places subtracted from the sum of the digits in the even places. Thus, 2948 = 2000 + 900 + 40+8= 2. (1001—1...
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