Happy Number!

Number Theory Level 2

Is 19 a happy number ?

A happy number is a number defined by the following process: Starting with any positive integer, replace the number by the sum of the squares of its digits in base-ten, and repeat the process until the number either equals 1 (where it will stay), or it loops endlessly in a cycle that does not include 1. Those numbers for which this process ends in 1 are happy numbers, while those that do not end in 1 are unhappy numbers (or sad numbers).

No Yes

Matin Naseri by Matin Naseri , 17, Afghanistan

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3 solutions

Venkatachalam J
Jan 2, 2018

If a positive integer, replace the number by the sum of the squares of its digits in base-ten and repeat the process until the number equals 1 are happy numbers. If it loops endless in a cycle that does not end in 1 are unhappy numbers.

2 Helpful 0 Interesting 0 Brilliant 0 Confused

Definition of a happy number should probably be included in the problem so it does not look like a bad joke to those who have not heard of it.

Marta Reece - 3 years, 5 months ago
Matin Naseri
Jan 2, 2018

Yes . Demonstration

(1 + 9)^2 = 82

(8 + 2)^2 = 68

(6 + 8)^2 = 100

(1 + 0 + 0)^2 = 1.

2 Helpful 0 Interesting 0 Brilliant 0 Confused
Ma Pm
Jan 2, 2018

1^2+9^2=82; 8^2+2^2=68; 6^2+8^2=100; 1^2+0^2+0^2=1

It's a happy number

0 Helpful 0 Interesting 0 Brilliant 0 Confused

Make it clearly please.

Matin Naseri - 3 years, 5 months ago

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