2020 AMC 10A Problems/Problem 22
Problem
For how many positive integers isnot divisible by ? (Recall that is the greatest integer less than or equal to .)
Solution 1
Let . If the expression isis not divisible by , then the three terms in the expression must be , which would imply that is a divisor of but not , or , which would imply that is a divisor of but not . has factors, and has factors. However, does not work because a divisor of both and , and since is counted twice, the answer is .
Solution 2
Let . Notice that if is divisible by , then the three terms in the expression must be , if is divisible by , then the three terms in the expression must be , and if if is divisible by , then the three terms in the expression must be .
Video Solution
~IceMatrix
See Also
2020 AMC 10A (Problems • Answer Key • Resources) | ||
Preceded by Problem 21 |
Followed by Problem 23 | |
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