Department of Mathematics, K.T.H.M. College, Nashik

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Registered: 23-07-2015

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Number Theory

Q.(Net June 2011) The number of elements in the set \(\{ m:1\leq m \leq 1000 \} \),where  m and 1000 are relatively prime is 

A) 100
B) 250
C) 300
D)400

Ans D
If n is any number then \(\phi (n) \)= number of relatively prime to n .

The number of elements in the \(\{ m:1\leq m \leq 1000 \} \) m and 1000 are relatively prime is 
\(\phi(1000)=1000(1-\frac{1}{2})(1-\frac{1}{5})=400 \)