 | Charles Davies - 1845 - 382 σελίδες
...— bm~l) of the remainder, be divisible by a — b, it follows that the dividend am — bm is also divisible by a — b : that is, If the difference of the same powers of two quantities be divisible by the difference of the quantities, then, the difference of the powers of a degree greater... | |
 | Scottish school-book assoc - 1845 - 444 σελίδες
...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 - 1846 - 542 σελίδες
...appears from this result, that a" — ft" will be exactly divisible by a — 6, if a°~' — 6°~l be divisible by a — b ; that is, if the difference...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 - 1846 - 380 σελίδες
...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... | |
 | Elias Loomis - 1846 - 376 σελίδες
...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... | |
 | Charles William Hackley - 1847 - 546 σελίδες
...result, that a" — 6" will be exactly divisible by a — b, if a"-' — 6°-' be divisible by a — 6; 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... | |
 | 1848 - 394 σελίδες
...remainder, be divisible by a — b, it follows that the dividend am — bm is also divisible by a — 6 ; that is, If the difference of the same powers of two quantities be divisible by the difference of the quantities, then, the difference of the powers of a degree greater... | |
 | Charles William Hackley - 1849 - 534 σελίδες
...appears from this result, that a" — 6" will be exactly divisible by — b, if a°~l — ti°~l be divisible by a — b; that is, if the difference of the same owers of two quantities is divisible by their difference, then the difference f the powers of the next... | |
 | Joseph Ray - 1848 - 250 σελίδες
...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, be divisible by the difference of... | |
 | Elias Loomis - 1855 - 356 σελίδες
...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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Now, if this remainder is divisible by a—b, it is obvious that the dividend is divisible by a — b; that is, if the difference of the same powers of two quantities is divisible by the difference of the quantities, then will the difference of the powers... 
