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How many integers \(n\) satisfy the condition \(100 < n < 200\) and the condition \(n\) has the same remainder whether it is divided by 6 or by 8?

 May 1, 2019
 #1
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+1

listfor(x, 100, 200, If(x % 6 ==x % 8, x, 0))

n =(100, 101,  120, 121, 122, 123, 124, 125,  144, 145, 146, 147, 148, 149, 168, 169, 170, 171, 172, 173, 192, 193, 194, 195, 196, 197) = 26 such numbers between 100 and 200.

 May 1, 2019
 #2
avatar+4594 
+1

We can also use modular arithmetic here.

 May 2, 2019

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