1978 AHSME Problems/Problem 27
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Problem 27
There is more than one integer greater than which, when divided by any integer such that , has a remainder of . What is the difference between the two smallest such integers?
Solution
Let this integer be . We have , , . Recall that if and then We see that since , , . We have
From to , contains the largest power of , contains the largest power of , and contains the largest power of . Thus, our lcm is equal to Since , our smallest values of are and The difference between these values is simply the value of
~JustinLee2017
See Also
1978 AHSME (Problems • Answer Key • Resources) | ||
Preceded by Problem 26 |
Followed by Problem 28 | |
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