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According to mathematical studies, a natural number is happy if the process of repeatedly summing the squares of its decimal digits finally ends in 1.
According to mathematical studies, a natural number is happy if the process of repeatedly summing the squares of its decimal digits finally ends in 1. For example, the least natural number (greater than 1) that is happy is 7, as shown here. 7 squared equals 49 comma 4 squared plus 9 squared equals 97 comma 9 squared plus 7 squared equals 130 comma 1 squared plus 3 squared plus 0 squared equals 10 comma 1 squared plus 0 squared equals 1 An amicable pair is a happy amicable pair if and only if both members of the pair are happy numbers. (The first 5000 amicable pairs include only 111 that are happy amicable pairs.) For the pair of amicable numbers 12 comma 285 and 14 comma 595, determine whether neither, one, or both of the members are happy, and whether the pair is a happy amicable pair. Question content area bottom Part 1 Is 12 comma 285 a happy number? A. Yes, 12 comma 285 is a happy number because the sum of the decimal digits eventually equals 1. B. No, 12 comma 285 is not a happy number because the sum of the squares of the decimal digits does not ever equal 1. C. No, 12 comma 285 is not a happy number because the sum of the decimal digits does not ever equal 1. D. Yes, 12 comma 285 is a happy number because the sum of the squares of the decimal digits eventually equals 1
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