Difference between revisions of "1951 AHSME Problems/Problem 15"
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== Solution == | == Solution == | ||
Factoring the polynomial gives <math>(n+1)(n)(n-1)</math> According to the factorization, one of those factors must be a multiple of two because there are more than 2 consecutive integers. In addition, because there are three consecutive integers, one of the integers must be a multiple of 3. | Factoring the polynomial gives <math>(n+1)(n)(n-1)</math> According to the factorization, one of those factors must be a multiple of two because there are more than 2 consecutive integers. In addition, because there are three consecutive integers, one of the integers must be a multiple of 3. | ||
| − | Multiplying the only factors that can be guaranteed gives <math>3\times2=\boxed{\ | + | Multiplying the only factors that can be guaranteed gives <math>3\times2=\boxed{\textbf{(E)} \ 6}</math> |
== See Also == | == See Also == | ||
Revision as of 23:09, 23 February 2013
Problem
The largest number by which the expression $n^3 \minus{} n$ (Error compiling LaTeX. Unknown error_msg) is divisible for all possible integral values of 
, is:
Solution
Factoring the polynomial gives 
According to the factorization, one of those factors must be a multiple of two because there are more than 2 consecutive integers. In addition, because there are three consecutive integers, one of the integers must be a multiple of 3.
Multiplying the only factors that can be guaranteed gives 
See Also
| 1951 AHSC (Problems • Answer Key • Resources) | ||
| Preceded by Problem 14 |
Followed by Problem 16 | |
| 1 • 2 • 3 • 4 • 5 • 6 • 7 • 8 • 9 • 10 • 11 • 12 • 13 • 14 • 15 • 16 • 17 • 18 • 19 • 20 • 21 • 22 • 23 • 24 • 25 • 26 • 27 • 28 • 29 • 30 • 31 • 32 • 33 • 34 • 35 • 36 • 37 • 38 • 39 • 40 • 41 • 42 • 43 • 44 • 45 • 46 • 47 • 48 • 49 • 50 | ||
| All AHSME Problems and Solutions | ||
