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15. How many non-negative integral value...

15. How many non-negative integral values of x satisfy the equation `[x/5] = [x/7] ? `

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It's clear that as n increases, `n/5`​ will eventually be much larger than `n/7`​
As long as the difference is at least 1, the integer parts can't be equal; a (very) little algebra gives us
`n/5​>=n/7​+1`
=`n>=35/2`
​so,there are five good values of n in [0,5) and three good values in the next continuous group of good values, in [7,10) (decreasing from 5 to 3, that is, by 7−5). also one in [14,15)
So the size of the solution set is `5+3+1=9`
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