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Question of the Day (18-May-17)

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The totient Φ(n) of a positive integer n is defined as the number of positive integers less than or equal to n that are co prime to n. It follows from the definition that Φ(1) = 1. Also, Φ(9) = 6 since there are six positive integers (1, 2, 4, 5, 7 and 8) less than 9 are co prime to 9. Which of the following relations holds true for Φ(n) if m and n are co prime?
 OPTIONS 1) Φ(m) + Φ(n) ≥ Φ(m + n) 2) Φ(m − n) ≤ Φ(m) − Φ(n) 3) Φ(m × n) = Φ(m) × Φ(n) 4) Φ(m + n) = Φ(m) + Φ(n) 5) Φ(m − n) > Φ2(m) − Φ(n)