1965 AHSME Problems/Problem 33
Problem
If the number , that is, , ends with zeros when given to the base and ends with zeros when given to the base , then equals:
Solution
We can use Legendre's Formula to find the number of s in base So . Likewise, we are looking for the number of s and s that divide , so we use Legendre's again. Thus, and So , and , which corresponds to answer .
~JustinLee2017
See Also
1965 AHSC (Problems • Answer Key • Resources) | ||
Preceded by Problem 32 |
Followed by Problem 34 | |
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