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Question 431642: PROBLEM 1:
A two digit number with 2 different digits has a special property: "When the sum of its digits is added to the product of its digits, the result is the number itself." What is the smallest number with this property?
PROBLEM 2:
Six is a perfect number because its factors ( not including 6)add up to itself. What are all the perfect numbers between 20 and 30?
Found 2 solutions by ankor@dixie-net.com, richard1234:
Answer by ankor@dixie-net.com(22740)   (Show Source):
You can put this solution on YOUR website! A two digit number with 2 different digits has a special property:
"When the sum of its digits is added to the product of its digits, the result is the number itself."
What is the smallest number with this property?
:
x = 10's digit
y = units
then
10x+y = the number
:
x + y + xy = 10x + y
xy = 10x - x + y - y
xy = 9x
y = 
y = 9 is the units
then
19 is the smallest number with this property.
:
See if that is true
1 + 9 + (1*9) = 10(1) + 9
:
:
PROBLEM 2:
Six is a perfect number because its factors ( not including 6)add up to itself. What are all the perfect numbers between 20 and 30?
28: 1 + 2 + 4 + 7 + 14
Answer by richard1234(7193)  (Show Source):
You can put this solution on YOUR website! 1. Suppose the number is  , where  . Then,  -->  -->  , b = 9. We can assume  to be as small as possible, so 19 is the smallest such number.
2. 28, because the sum of its proper divisors is 1+2+4+7+14 = 28. In fact, all even perfect numbers are in the form  where  is prime. This is because the sum of divisors function is a multiplicative function for relatively prime integers. When  ,  , prime, so  , a perfect number.
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