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" IF the difference of the same powers of two quantities is divisible by the difference of the quantities... "
The Normal Elementary Algebra: Containing the First Principles of the ... - Page 64
by Edward Brooks - 1888 - 154 pages
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A system of practical mathematics; being no.xvi. of a new series of school-books

Scottish school-book assoc - 1845 - 444 pages
...of the quantities themselves, whether the exponents be even or odd. See 1st and 3d. 39. THEOREM II. The difference of the same powers of two quantities is divisible by the sum of the quantities without a remainder, if the exponent be even, but not if the exponent be odd....
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A Treatise on Algebra: Containing the Latest Improvements. Adapted to the ...

Charles William Hackley - Algebra - 1846 - 542 pages
...— I" will be exactly divisible by a — 6, if a"" 1 — 6°~' be divisible by a — b ; that is, if the difference of the same powers of two quantities is divisible by their difference, then the difference of the powers of the next higher degree is also divisible by...
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A Treatise on Algebra

Elias Loomis - Algebra - 1846 - 376 pages
...a"-i — 6n-i is divisible by a — b, an — 6n will also be divisible by a — b. That is to say, if the difference of the same powers of two quantities is divisible by their difference, the difference of the powers of the next higher degree is also divisible by that...
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A Treatise on Algebra

Elias Loomis - Algebra - 1846 - 380 pages
...an~l — 6"-1 is divisible by a — 6, a" — bn will also be divisible by a — b. That is to say, if the difference of the same powers of two quantities is divisible by their difference, the difference of the powers of the next higher degree is also divisible by that...
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Ray's Algebra, Part First: On the Analytic and Inductive Methods of ..., Part 1

Joseph Ray - Algebra - 1848 - 252 pages
...divisible by a — 6, then will a"1 — bm be also divisible by it. That is, IF the difference of ike same powers of two quantities is divisible by the difference of the quantities themselves, then will the difference of the next higher powers of the same quantities, be...
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Ray's Algebra Part Second: An Analytical Treatise, Designed for High Schools ...

Joseph Ray - Algebra - 1852 - 408 pages
...a"1"' — Jm~' is divisible by a — b, then will a™ — im,be divisible by a — b. That is, IF the difference of the same powers of two quantities is divisible by the difference of the quantities themselves, then will the difference of the next higher powers of the same quantities, be...
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Ray's Algebra, Part First: On the Analytic and Inductive Methods of ...

Joseph Ray - Algebra - 1848 - 250 pages
...is divisible by a — b, then will am—bm be also divisible by it. That is, IF the difference oflfu same powers of two quantities is divisible by the difference of the quantities themselves, then will tlie difference of the next higher powers of the same quantities,...
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A Treatise on Algebra

Elias Loomis - Algebra - 1855 - 356 pages
...remainder is divisible by a—b, it is obvious that the dividend is divisible by a—b. That is to say, if the difference of the same powers of two quantities is divisible by then difference, the difference of the powers of the next higher degree is also divisible by that difference....
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New University Algebra: A Theoretical and Practical Treatise, Containing ...

Horatio Nelson Robinson - Algebra - 1864 - 444 pages
...+Ь-(а«--_Ь"-» ) = + Ь»(ав— J°)=+im(l— 1) = 0 and the division in this case will be exact. Hence, The difference of the same powers of two quantities is divisible by the sum of the quantities, if the exponent is even, but not otherwise. 4. — Divide a" — 6" by a —...
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Ray's Algebra, Part Second: An Analytical Treatise, Designed for ..., Part 2

Joseph Ray - Algebra - 1852 - 420 pages
...IF a™~' — 4m~' is divisible by a — b, then will a1"— 6m,be divisible by a — 4. That is, IF the difference of the same powers of two quantities is divisible by the difference of the quantities themselves, then win the difference of the next higher powers of the same quantities, be...
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