2-digit Num3ers | DigitSum and DigitProduct

 
Let   ab   be a 2-digit number

DigitSum (ab)   =   a   +   b
DigitProduct (ab)   =   a * b

N   =   10*a   +   b   –   (a + b)   =   9*a
M   =   10*a   +   b   +   (a * b)

The numbers   10,   11,   12,   …   ,   19

N   =   9   =   3^2   is a perfect square
M   =   10*1 + 3 + (1 * 3)   =   16   =   4^2   is a perfect square
Only   ab = 13   we get a perfect square
where   10   <   ab   <   19

 

With the numbers   40,   41,   42,   …   ,   49

N   =   9*4   =   36   =   6^2   is a perfect square
 

With the numbers   90,   91,   …   ,   99

N   =   9^2   is a perfect square

When   ab = 91   we get a perfect square:
M   =   10*9   +   1   +   (9 * 1)   =   100   =   10^2   is a perfect square

 

With the numbers   30,   31,   …   ,   39

N   =   3^3   is a perfect cube

 
 
 
 

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About benvitalis

math grad - Interest: Number theory
This entry was posted in Math Beauty, Number Puzzles and tagged , . Bookmark the permalink.

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