| 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.... | |
| 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... | |
| 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... | |
| 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... | |
| 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... | |
| 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... | |
| 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,... | |
| 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.... | |
| 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 —... | |
| 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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